I went to Soldiers & Sailors online for the name Charles Tompkins and got these units with a man bearing that name:

4th Iowa Inf - in the 1865 NC Campaign
11th Michigan Inf - not in the NC campaign
121st NY Inf - not in the NC campaign
57th NY Inf - mustered out late 1864
1st Ohio Lt Arty - Battery C & D served in the 1865 NC Campaign
5th Iowa Cavalry - not in NC campaign
17th PA Cav - not in NC campaign
3rd US Inf - not in NC campaign
57th PA Inf - not in NC campaign
26th PA Inf - mustered out July 1864

The flag's provenance states it was Charles H. Tompkins - and these units had such a man:

1st Vermont Cav - not in the NC campaign
1st US Dragoons (became one of the regular cav regiments) - not in NC campaign
2nd Battalion Reserve Corps
1st Rhode Island Heavy Artillery - not in the NC campaign
5th Rhode Island Heavy Artillery - served in NC into June, 1865 in the New Bern area

There were some New York cavalry units that operated in North Carolina independently of the main Union forces of 1865 but I have not chased down which ones did that and when. I know a couple flags in the New York Military Museum were taken by these units.

I am not sure what to think about this flag's stated provenance but the name does not connect well with New York and North Carolina service.

Greg Biggs