To get back to the main topics, here are the flag I would addopt
Cilgov flag would be made with the presidential flag with the eagle looking at the olive branch while Milgov flag would be made from a presidential flag with an eagle looking at the arrows. They are very similar but I agree with Chico and Kato. Both make a statement for legitimacy and I like the silght difference noted by Kato (actually I didn't even noticed it when I designed these flags

; very good one Kato)
I picked up the idea of a confederate sovereign state (as I like that idea) and, of course, they are using the late confederate flag as they are also looking for some kind of legitimacy.
For New America, I simply used the Bonnie-Blue Flag as Chico reminded me of the blue arm band worn by New America in the Ozarks.
In my game I have an Allegheny Free State and used for it a modified flag from the Allegheny City Guard (I just find it very nice

)