POWER OF ATTORNEY
                                      FOR
                  KAYNE ANDERSON MIDSTREAM/ENERGY FUND, INC.
                             SECTION 16(a) FILINGS

    Know all by these presents, that the undersigned hereby constitutes and
appoints David J. Shladovsky, Terry A. Hart, James C. Baker and David A. Hearth
as the undersigned's true and lawful attorneys-in-fact to:

    (1) Execute for and on behalf of the undersigned, in the undersigned's
        capacity as a director and/or shareholder of Kayne Anderson
        Midstream/Energy Fund, Inc., a Maryland corporation (the "Company"),
        Form IDs and Forms 3, 4, and 5 and amendments thereto in accordance with
        Section 16(a) of the Securities Exchange Act of 1934 (the "Exchange
        Act"), and the rules promulgated thereunder;

    (2) Do and perform any and all acts for and on behalf of the undersigned
        which may be necessary or desirable to complete and execute any such
        Form IDs and Form 3, 4, or 5 or amendment thereto and timely file such
        forms with the United States Securities and Exchange Commission (the
        "SEC") and any stock exchange or similar authority, as required; and

    (3) Take any other action of any type whatsoever which, in the opinion of
        any such attorney-in-fact, may be of benefit, in the best interest of,
        or legally required by, the undersigned, it being understood that the
        documents executed by such attorney-in-fact on behalf of the undersigned
        pursuant to this Power of Attorney shall be in such form and shall
        contain such terms and conditions as such attorney-in-fact may approve.

    The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this Power of Attorney and the rights and powers herein
granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Exchange Act.

    This Power of Attorney shall remain in full force and effect with respect to
the undersigned until the earliest to occur of (a) the undersigned is no longer
required to file Forms 3, 4, and 5 with respect to the undersigned's holdings of
and transaction in securities issued by the Company or (b) revocation by the
undersigned in a signed writing delivered to the Company and each of the
foregoing attorneys-in-fact. This Power of Attorney shall terminate with respect
to a foregoing attorney-in-fact, individually, at such time as such attorney-in-
fact is no longer employed or engaged by the Company or any of its subsidiaries.
This Power of Attorney may be filed with the SEC as a confirming statement of
the authority granted herein.

    IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 31st day of July, 2018.

                                        Anne K. Costin
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                                        Print Name of Reporting Person or Entity


                                        /S/ ANNE K. COSTIN
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                                        Signature