Ryan,
There is/was, another Van Dorn flag that had a battle honor on it. This was once in the Iowa state collection but cannot be located today. As follows:
No. 92 - Confederate Van Dorn pattern flag, captured at Big Black by Pvt. David Burkhart, Co. A, 23rd Iowa. "Elkhorn" on flag.
This is probably the flag of the 21st Arkansas Infantry.
Greg Biggs