I found this out researching my family members that were in the 6th Michigan Inf, later the 6th Michigan HA (they were allowed to keep there Inf name)
At the battle of Baton Rouge, according to the "History of the 6th Michigan Infantry" they captured the 9th La Bttn's flag.
I have not a clue what the 9th La' bttn flag looked liked. But I have a book on every Louisiana organization.
Compendium of the Confederate armies---Louisiana by Stewart Sifakis.
The 9th La Bttn aka 17th Infantry Battalion. Indeed they did fight at Baton Rouge on August 5th, 1862.