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 Domestic Accounts Receivable of Inventory.

+ References

No definition available.

+ Details

Name:	FSI_PercentageOfDomesticAccountsReceivableOfInventory
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/exampleRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 55
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482949/835-30-55-8

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69B

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69C
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69C

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482900/835-30-50-1

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482925/835-30-45-2

+ 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

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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481544/470-10-50-6

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 470
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481544/470-10-50-6

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(f))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

+ 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

+ 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://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 852
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481372/852-10-55-10

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

+ Details

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

- Details

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

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_NoncontrollingInterestMember
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:	dei_LegalEntityAxis=FSI_NanoChemSolutionIncMember
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_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:

SHORT-TERM LINE OF CREDIT (Details Narrative) - USD ($)	1 Months Ended
SHORT-TERM LINE OF CREDIT (Details Narrative) - USD ($)	Aug. 31, 2024	Jun. 30, 2024	Sep. 30, 2024	Dec. 31, 2023
Line of Credit Facility [Line Items]
Line of credit				$ 1,810,479
Stock Yard And Bank One [Member] \| Noncontrolling Interest [Member]
Line of Credit Facility [Line Items]
Loan guaranteed rate			35.00%
Line of credit			$ 1,575,000
Stock Yard And Bank One [Member] \| New Agreement [Member] \| NanoChem Solutions Inc [Member]
Line of Credit Facility [Line Items]
Loan guaranteed rate			65.00%
Line of credit			$ 2,925,000
Short term borrowings				$ 1,810,479
Stock Yard And Bank One [Member] \| Midland States Bank [Member] \| New Agreement [Member]
Line of Credit Facility [Line Items]
Aggregate amount of revolving line of credit		$ 4,500,000
Percentage of domestic accounts receivable of inventory		50.00%
Debt face amount		$ 2,000,000
Interest rate			8.00%	8.50%
Stock Bank [Member] \| New Agreement [Member] \| NanoChem Solutions Inc [Member] \| Revolving Credit Facility [Member]
Line of Credit Facility [Line Items]
Short term borrowings
Stock Bank [Member] \| Midland States Bank [Member] \| New Agreement [Member]
Line of Credit Facility [Line Items]
Aggregate amount of revolving line of credit	$ 2,000,000
Debt face amount	$ 1,000,000
Interest rate			8.00%	8.50%
Eligible percentage of domestic accounts receivable	50.00%