<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-01-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001419600</issuerCik>
        <issuerName>Flexion Therapeutics Inc</issuerName>
        <issuerTradingSymbol>FLXN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001369453</rptOwnerCik>
            <rptOwnerName>Wentworth Kerry</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FLEXION THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>10 MALL ROAD, SUITE 301</rptOwnerStreet2>
            <rptOwnerCity>BURLINGTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01803</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Regulatory Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-01-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6829</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.13</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>113767</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Sale of shares of common stock to cover tax withholding obligations associated with the vesting of restricted stock unit awards granted to the Reporting Person on February 1, 2018, March 1, 2019, and March 2, 2020.</footnote>
        <footnote id="F2">The weighted average sale price for the transaction reported was $11.13. The shares were sold at a range of prices between $11.12 and $11.57.  Upon request by the SEC staff, the Issuer, or any security holder of the Issuer, full information regarding the number of shares sold at each separate price will be provided.</footnote>
        <footnote id="F3">Includes 416 shares of common stock that were acquired by the Reporting Person on December 20, 2020, at $9.77 per share pursuant to the Issuer's Employee Stock Purchase Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Mark S. Levine, Attorney-in-Fact</signatureName>
        <signatureDate>2021-01-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
