Exhibit
32.1



CERTIFICATIONS
OF PRINCIPAL EXECUTIVE OFFICER AND PRINCIPAL FINANCIAL OFFICER

PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

(18
U.S.C. § 1350)



Pursuant
to Section 1350, Chapter 63 of Title 18, United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of
2002, each of the undersigned officers of Flat Rock Capital Corp. (the “Company”), does hereby certify, for
purposes of Section 1350 of Chapter 63 of Title 18 of the United States Code, as adopted pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002 that, to the undersigned’s knowledge:



| | 1) | the
                                         Company’s Annual Report on Form 10-K for the year ended December 31, 2018 (the
                                         “Report”) fully complies with the requirements of Section 13(a) or 15(d),
                                         as applicable, of the Securities Exchange Act of 1934, as amended; and
| | -- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



| | 2) | the
                                         information contained in the Report fairly presents, in all material respects, the financial
                                         condition and results of operations of the Company.
| | -- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



|Date: | March
    13, 2019 | By:                                                                                 | /s/
    Robert K. Grunewald  
|----- | ------------------ | ----------------------------------------------------------------------------------- | -----------------------------
|      |                    | Robert
    K. GrunewaldPresident and Chief Executive Officer                       
|      |                    | (Principal
    Executive Officer)                                                  
|      |                    |                                                                                    
|Date: | March
    13, 2019 | By:                                                                                 | /s/ Richard
    A. Petrocelli
|      |                    | Richard
    A. Petrocelli                                                          
|      |                    | Chief
    Financial Officer andChief Operating Officer(Principal Financial Officer)



The
foregoing certification is being furnished with the Company’s Annual Report on Form 10-K pursuant to 18 U.S.C. Section 1350.
It is not being filed for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, and it is not to be incorporated
by reference into any filing of the Company, whether made before or after the date hereof, regardless of any general information
language in such filing, except to the extent that the Company specifically incorporates by reference.



A
signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the
Company and furnished to the Securities and Exchange Commission or its staff upon request.