I am doing the book on Tennessee Civil War flags for the state museum and I have found no existing flag for Baxter's Battery - nor for most of the many TN artillery units for that matter.
I own the book on Baxter's Battery and cannot locate anything in it describing the flag they used other than Page 222 - which is not sourced. I highly doubt it looked like the flag in that page - it might not have even been a Second National at all unless the author had a description of the flag that was not used in the book. I doubt it had a "2' on it or crossed cannons and may have had the unit name.
The battery may also have used a First National flag as well since it formed before the May, 1863 adoption of the Second National.
Unless I see a source for the flag on Page 222 I will have doubts as to its accuracy.