Sounds very much like a Virginia Military Institute flag.
The one carried by the Cadets at New Market in May 1864 was destroyed in June 1864 to prevent "Black Dave" Hunter from capturing it. This flag design was first issued to the VMI in 1850 and a newer flag was issued in 1859, both flags were made by Horstman's. This flag was later reproduced and the reproduction bears little in common with the flag in question.
However, what was the VMI using from its formation in 1839 until the issue of 1850?
Is it possible an earlier version with a different design was 'retired' and held in some location in the Valley? Was this location 'visited' by Custer and his arsonists in 1864 and the flag in question taken then?
Possibly someone with details on Horstman's production and/or the history of VMI flags can provide answers.