Just because a unit was in Virginia does not mean they got ANV battle flags from the Richmond Depot. You had to be an actual aprt of Lee's army to get one of those and I belive the battery did not join that army until much later after their arrival into the state. A large number of units that fought in Virginia from its toe up through the valley did not have ANV battle flags as they were in a different department (Dept. of Western VA and Dept. of SW Va) and it was rare for QM depots to cross departmental lines, which is why each department had its own depots for the most part. In the case of this area of VA, it was the Staunton Depot.
Staunton Depot battle flags were inspired by the ANV flags but built differently. There's a picture of one for comparions in the Time-Life book "Arms & Equipment of the Confederacy."
If this battery did, in fact, join the ANV directly in the Fall of 1863 they might well have gotten a Third Bunting Richmond Depot battle flag but my sources state they did not join that army until 1865.
Does Jeff Weaver have something different?