If that flag is still attached to the backing that Amelia Fowler and her girls stitched it to then I think it would be very difficult to determine just what was on the reverse except by comparison with other period flags. The State Library of Massachusetts, located in the basement of the State House in Boston has the Fowler files, which were transferred there from the US Park Service at Harper's Ferry some years ago. Perhaps they took a photo of the reverse prior to the "preservation" project.

Here is the reference to the collection:
Ms. Coll. 61
Title: Amelia Fowler and Katherine Fowler Richey Papers, 1927-1976
8 boxes
Creator: Fowler, Amelia Bold (1862-1923) and Richey, Katherine Fowler (1889-1949)

Good luck.
Nick Artimovich