Sorry for the delay, I wanted to respond quicker but we've had internet issues here.....anyway, That account comes from the Thomas L Sullivan Account Book, at the TN State Library & Archives (Civil War Collection, Thomas L Sullivan Account Book, IV, B-6, Box 28). I have a photocopy if you'd like me to send you a copy of it.
I agree, this unit was moving up from GA to rejoin the Army of TN in March of '65. The diary mentions going through Augusta, then Edgefield, and eventually they join the army in NC. What I quoted is the only mention of the flag. I am very curious about it, and hope you can identify the unit.
I checked the online CWSS and it listed about ten Thomas Sullivans.
Let me know if I can be of more help,
Bert