Looks like the 17th&23rd Tennessee lost a flag there as well. The War Department returned this flag.

Hardee pattern battle flag (37x40)

"Captured before Petersburg, Virginia, June 1864 by the 9th U.S Army Corps." (War Department #144)

Another flag was captured:

Army of Northern Virginia pattern battle flag, orange boarder (48x47). Captured at Petersburg, Virginia, June 1864 by Private John H. Harbourne, 29th Massachusetts Veteran Volunteer Infantry. (War Department #146)

63rd Tennessee's flag:
Army of Northern Virginia pattern battle flag.
(48 1/2x 44 1/2)
Captured at the battle of Petersburg, Virginia, June 1864 by Pvt. Henry W. Rowe, 11th New Hampshire Infantry.
(War Department #147)

Looks like they are missing War Department #145. I don't see a listing for the 44th Tennessee either.

I did find that the 25th&44th Tennessee lost a flag on April 1865. (Petersburg)

Army of Northern Virginia pattern battle flag.
(47 1/2x 49 1/2)
Flag was captured by Cpl. Milton Blickensderfer, 126th Ohio Infantry. (War Department #344)

Have a great weekend,

Shawn