Ken and everyone,
In checking the service areas of the 6th Georgia Cavalry, they never served in the ANV nor the District of North Carolina. They did serve in th Department of East TN (probably with a First National flag) until August 1863 whereupon they became part of Forrest's Cavalry Corps for Chickamauga, etc. When Forrest went to Mississippi the 6th GA Cavalry and other units became part of Wheeler's Cavalry Corps and in 1864 they should have been issued an Augusta Depot battle flag.
Now - having said the above, there is a flag requisition for the 6th GA Cavalry dated May 1863 where they received one battle flag while in Morristown which is in East Tennessee. So what was this flag? I have never heard of a unit outside of VA or NC getting a Richmond Depot flag that I can recall but who knows.
One brigade of Wheeler's Corps did picket Lay's Ferry when the Federals initially crossed the river. They got reinforced by at least one brigade of WHT Walker's Division during the May days in question.