It is very difficult finding accurate color info for a subject that old. Even if color photography existed then, the aging of negatives would make the color suspect. Sometimes you can see, in black and white photos, how dark or light a gray is by comparing it to objects whose color appearance you know.
The good thing is, whatever color you decide to go with, others will have a hard time proving you wrong :-)
You might try to find a civil war re-enactment group in your area. They are pretty knowledgeable about uniforms, and fabrics may hold their color far better than any paint.