There is a remote possibility that newspapers of the period may report on captured Union flags brought to Richmond and displayed. The Richmond Daily Dispatch, as an example, has now been placed on-line. It describes, but does not identify, Union flags displayed other than at the War Department (former Mechanics' Institute or Hall) or in the Executive Mansion ("White House of the Confederacy"), namely, Libby Prison! Here's a clip from the 4 Apr 1863 issue:

"The walls of the office at the Libby Prison are now adorned with a large number of flag[s] captured from United States troops, among which are five fine silk ones and two guid[o]ns. The flags are of the Star and Stripe pattern, and one of them taken at Vicksburg is spattered with blood."