Hi,
That "flag" or badge/insignia, was adopted by Union General James H. Wilson in 1864 for his "Wilson's Cavalry Corps". The insignia consisted of a "carbine from which was suspended, by chains, a red Swallow-tailed guidon, bearing gilt crossed sabres". All of the army corps adopted distinctive badges with just two exceptions, the Thirteenth and Twenty-First Corps. Badges were first authorized to be used by the Army of the Potomic on July 21, 1863.
The flag is historically correct. I would think it's very appropriate to represent the Spencer Shooting Society.
Two Flints