Nevada did not officially become a State until July 4, 1865 but its admission by Congress was on October 31, 1864. A lot of flag makers jumped the gun and added the 36th star, so any of the nationals made in 1864 could have 36 stars.

The Federal Troops in Nevada about this time were mostly company strength so a Regiment or Regimental National flag would not be in their possession only company guidons.

I suggested West Virginia because they had the larger number of new regiments forming and would have received several 36 star flags.

On your Hospital flags, the archives may have changed their site, in that case you might have to make a visit or go through you local library and request research material from the National archives.

Since the flag in your picture is a dark color I would guess that it is red. I’m guessing that the men in the picture are about 5 feet tall, so the flag is about 3x4’

Happy Trails!
Tom Martin