While I am unfamiliar with the fragment of the 23rd VA flag at Appomattox. I have seen an intact flag of the 23rd VA at the Museum of the Confederacy in Richmond, VA. The flag is currently undergoing a procedure to help conserve it.
Hope this helps.
Paul B. Boulden Jr.
RAH VA MIL '04
Member 23rd VA Vol. Regt. Living History organization