The Anderson Battery, aka Boutetort Artillery, brought two flags with them. One was their 1861 Virginia state flag that, according to what I have, was torn up on July 3rd so that it would not be surrendered. The battery name was on the flag. They then surrendered a "battle flag," but what that actually was might be problematic based on their area of service prior to coming to Mississippi with Stevenson's Division. The only time they served in the Eastern Theater was from December 1861-January 1862 as part of Johnson's Army of the Northwest.
They then became part of Stevenson's Division operating in East Tennessee as part of the Department of East Tennessee from May through December 1862. I have found, as did the late Howard Madaus, that ANV flags from the Richmond Depot were sent to some of the units operating in that department but who got them and how many we don't completely know. I did a survey of QM documents from QM officers that were in East Tennessee and found that they drew supplies from Abington, Salem and Richmond, VA. so getting ANV flags from the Richmond Depot was not hard to do - just look at where their railroad went for one.
Stevenson's Division became part of the Army of Tennessee after the Kentucky Campaign of 1862 for a brief time when, in November, they were sent to Vicksburg from Middle Tennessee. And there they served until the surrender of July.
So what flag did they carry? Could have been an ANV - could have been something else. Sgt./Lt. Obenchain of the battery stated that two Federal officers took their "battle flag" at the surrender. He also stated they no longer used the state flag as it had the name of their former commander, Anderson, on it (Anderson's Battery) and this is the one they tore up on July 3rd.