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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-11-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001723701</issuerCik>
        <issuerName>PIMCO Flexible Municipal Income Fund</issuerName>
        <issuerTradingSymbol>PMFLX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000835271</rptOwnerCik>
            <rptOwnerName>JPMorgan Chase Bank, N.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1111 POLARIS PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>COLUMBUS</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>43240</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Variable Rate MuniFund Term Preferred Shares, Series 2050-B</value>
            </securityTitle>
            <transactionDate>
                <value>2022-11-01</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>250</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                    <footnoteId id="F1"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1000</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The 250 variable rate munifund term preferred shares reported as acquired in Table I represent variable rate munifund term preferred shares, series 2050-B (the &quot;VMTP Shares&quot;) beneficially owned by JPMorgan Chase Bank, National Association (&quot;JPMCB&quot;) that were acquired from the Issuer at a price of $100,000 per share.</footnote>
        <footnote id="F2">In addition to the 250 VMTP Shares reported as acquired in Table I above by JPMCB, JPMCB holds 750 VMTP Shares of the Issuer.  The 750 VMTP Shares were previously acquired by JPMCB as reported in the Form 3 filing filed by JPMCB with the United States Securities and Exchange Commission filed October 8, 2020.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Sean Saroya</signatureName>
        <signatureDate>2022-11-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
