We know for a fact that several ANV flags equipped units of the Army of Tennessee in the Atlanta campaign. The four Texas regiments of Ector's Brigade had ANV Fourth Bunting flags thanks to one of their officers who was in Richmond in May 1864 and brought them back. This was noted in the Texas flags book of Robert Maberry.
At least three ANV Third Bunting flags were also in the AOT for units that had either been in the ANV itself or in the District of North Carolina which was, according to Madaus, supplied by the Richmond Depot. As follows:
26th Alabama Infantry (ADAH collection)
47th Georgia Infantry (possibly) (Lay's Ferry capture)
66th Georgia Infantry (probably) (Battle of Atlanta capture) (ghas also been listed as the 25th, 29th or 30th Georgia)