Eligible percentage of domestic accounts receivable.

No definition available.

Name:	FSI_EligiblePercentageOfDomesticAccountsReceivable
Namespace Prefix:	FSI_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Loan guaranteed rate.

+ References

No definition available.

+ Details

Name:	FSI_LoanGuaranteedRate
Namespace Prefix:	FSI_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Percentage of foreign accounts receivable of inventory.

+ References

No definition available.

+ Details

Name:	FSI_PercentageOfForeignAccountsReceivableOfInventory
Namespace Prefix:	FSI_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1B
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=123466505&loc=SL123495323-112611

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=124435984&loc=d3e28551-108399

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 55
-Paragraph 8
-URI https://asc.fasb.org/extlink&oid=114775985&loc=d3e28878-108400

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124429444&loc=SL124452920-239629

Reference 5: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69C
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495737-112612

Reference 6: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69B
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495735-112612

+ Details

Name:	us-gaap_DebtInstrumentFaceAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The effective interest rate at the end of the reporting period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The effective interest rate during the reporting period.

+ References

+ Details

Name:	us-gaap_LineOfCreditFacilityInterestRateDuringPeriod
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_LineOfCreditFacilityLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

+ Details

Name:	us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The carrying value as of the balance sheet date of the current portion of long-term obligations drawn from a line of credit, which is a bank's commitment to make loans up to a specific amount. Examples of items that might be included in the application of this element may consist of letters of credit, standby letters of credit, and revolving credit arrangements, under which borrowings can be made up to a maximum amount as of any point in time conditional on satisfaction of specified terms before, as of and after the date of drawdowns on the line. Includes short-term obligations that would normally be classified as current liabilities but for which (a) postbalance sheet date issuance of a long term obligation to refinance the short term obligation on a long term basis, or (b) the enterprise has entered into a financing agreement that clearly permits the enterprise to refinance the short-term obligation on a long term basis and the following conditions are met (1) the agreement does not expire within 1 year and is not cancelable by the lender except for violation of an objectively determinable provision, (2) no violation exists at the BS date, and (3) the lender has entered into the financing agreement is expected to be financially capable of honoring the agreement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_LinesOfCreditCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Reflects the total carrying amount as of the balance sheet date of debt having initial terms less than one year or the normal operating cycle, if longer.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 852
-SubTopic 10
-Section 55
-Paragraph 10
-URI https://asc.fasb.org/extlink&oid=84165509&loc=d3e56426-112766

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19)(a))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(1))
-URI https://asc.fasb.org/extlink&oid=126734703&loc=d3e572229-122910

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

+ Details

Name:	us-gaap_ShortTermBorrowings
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	dei_LegalEntityAxis=FSI_NanoChemSolutionIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LineOfCreditFacilityAxis=FSI_StockYardAndBankMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_TypeOfArrangementAxis=FSI_NewAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LineOfCreditFacilityAxis=FSI_StockBankMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_RevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=FSI_MidlandStatesBankMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LineOfCreditFacilityAxis=FSI_HarrisBankMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=FSI_HarrisBankMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=FSI_TermLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

SHORT-TERM LINE OF CREDIT (Details Narrative) - USD ($)	1 Months Ended
SHORT-TERM LINE OF CREDIT (Details Narrative) - USD ($)	Jun. 30, 2022	Mar. 31, 2022	Oct. 31, 2021	Dec. 31, 2022	Sep. 30, 2022	Dec. 31, 2021
Line of Credit Facility [Line Items]
Line of credit				$ 2,818,591		$ 2,300,819
Interest rate				3.00%
NanoChem Solutions Inc [Member] \| Stock Yard And Bank One [Member]
Line of Credit Facility [Line Items]
Loan guaranteed rate	35.00%
Line of credit	$ 1,400,000
New Agreement [Member] \| NanoChem Solutions Inc [Member]
Line of Credit Facility [Line Items]
Loan guaranteed rate		65.00%
Line of credit		$ 2,600,000
New Agreement [Member] \| NanoChem Solutions Inc [Member] \| Stock Yard And Bank One [Member]
Line of Credit Facility [Line Items]
Loan guaranteed rate	65.00%
Line of credit	$ 2,600,000
Short term borrowings				$ 2,477,794
New Agreement [Member] \| NanoChem Solutions Inc [Member] \| Stock Bank [Member] \| Revolving Credit Facility [Member]
Line of Credit Facility [Line Items]
Short term borrowings				340,797
Midland States Bank [Member] \| New Agreement [Member]
Line of Credit Facility [Line Items]
Aggregate amount of revolving line of credit		$ 4,000,000
Debt effective rate		1.00%	0.50%
Annual interest rate of loan						4.25%
Short term borrowings						$ 811,665
Midland States Bank [Member] \| New Agreement [Member] \| Harris Bank [Member]
Line of Credit Facility [Line Items]
Aggregate amount of revolving line of credit			$ 3,500,000
Annual interest rate of loan						4.50%
Line of credit						$ 1,489,154
Eligible percentage of domestic accounts receivable			80.00%
Percentage of foreign accounts receivable of inventory			50.00%
Midland States Bank [Member] \| New Agreement [Member] \| Stock Yard And Bank One [Member]
Line of Credit Facility [Line Items]
Aggregate amount of revolving line of credit	$ 4,000,000
Percentage of foreign accounts receivable of inventory	50.00%
Interest rate				7.50%
Debt face amount	$ 2,000,000
Midland States Bank [Member] \| New Agreement [Member] \| Stock Bank [Member]
Line of Credit Facility [Line Items]
Aggregate amount of revolving line of credit	$ 4,000,000
Eligible percentage of domestic accounts receivable	80.00%
Percentage of foreign accounts receivable of inventory	50.00%
Interest rate					7.50%
Debt face amount	$ 2,000,000
Midland States Bank [Member] \| New Agreement [Member] \| Maximum [Member]
Line of Credit Facility [Line Items]
Annual interest rate of loan		4.25%
Harris Bank [Member] \| NanoChem Solutions Inc [Member] \| Term Loan [Member]
Line of Credit Facility [Line Items]
Interest rate			4.50%