Ben,
Is the flag square or rectangular? I observed a flag very similar to what you describe on display at the Old Courthouse Museum in Vicksburg. It is 45" to 48" square (as they say, some losses), approximately 5" blue saltaire, no fimbration, 12-3" to 3-1/2" white stars. In the hoist quadrant it is lettered "21st REGT/ MISS/ VOLS". Dont know if there is a connection, but when I read your description, this flag came to mind.
Charles