Thanks guys for the leads.
I found the flag on the NC State Museum of History website. The description doesn't mention Lynchburg anywhere.
I check Barringer's career during the war and it doesn't appear that he was at the Battle of Lynchburg. (that cavalry was a small command under Imboden and McCausland).
So I tend to want to discount the Barringer flag as having anything to do with Lynchburg.
Does anyone know where its connection to Lynchburg comes into play?
I still want to get a look at the Lynchburg captured flag in West Virginia.