I would believe the flag in use at the time of the Vicksburg surrender of July 4, 1863, would still be labled at that of the 31st Tennessee Infantry.

In June, 1863, the East Tennessee Regiment was officially designated as the 39th Tennessee Infantry Regiment, but prior to that time it was known as W. M. Bradford’s 31st. The regiment was organized at Knoxville, Tennessee March 28, 1862.

There may be a SCV Camp located in the Knoxville area which may have knowledge of the flag.