Tony,
You may have seen it already but here's the museum worksheet of the 3rd Artillery's Battleflag.

http://ncmuseumofhistory.org/MOH/vfpcgi.exe?IDCFile=/moh/DETAILS.IDC,SPECIFIC=6248,DATABASE=69189281,

The organization of the 40th N.C.T./3rd Artillery began in January 1862, but was first completed at Fort Holmes, Smith's Island, on December 1, 1863. The individual companies of this regiment saw action at Forts Anderson and Fisher and during the Carolinas Campaign of 1865. Most of the companies fought their last battle at Bentonville, N.C., March 19-21, 1865.
The silk flag is handsewn. 22 1/2" (hoist) x 21 5/8" (fly). Thirteen 3 3/16" stars.