There are personnel files for DC police officers including the time period of his death included in RG 351.5 https://www.archives.gov/research/guide-fed-records/groups/351.html#351.5
The DC health Dept (Vital records) started keeping death certificates in August 1874.
Images of the death certificate are available at your local Family History Center (once they re-open) by going to https://www.familysearch.org/search/image/uri=https://familysearch.org/recapi/sord/collection/1803967/waypoints
the following appeared on myheritage.com
Name Robert Fleet Gender Male Birth Marital status Married Death Burial Occupation Policeman Race Black Ethnicity American Race Black
This burial notice was in the Evening Star newspaper 24 Aug 1874
Dear Mr. Breul,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located Personnel Case Files, 1861 -1950; Register of Appointments, 1861 - 1930; and the Service Records, 1861 -1930 of the Metropolitan Police in the Records of the Government of the District of Columbia (Record Group 351) that may include a file or files for Robert Fleet. For access to these records, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at firstname.lastname@example.org
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1. We apologize for this inconvenience and appreciate your understanding and patience.
We hope this is helpful. Best of luck with your research!