The diary doesn't specifically mention the flag.
But what Sgt Miers did say is that when they left the camp that the soldiers were told to carry only 35 pounds in their packs. Everything else was left behind for the Quartermaster corp to pick up. That included their tents, personal and company baggage. Miers commented that he had to leave behind two good suits.
That would explain why any "Extra" Flag would have been left with the baggage where it was reported as be "Captured" "In a Trunk" when the Union Gunboat landed a raiding party and burned the camp. This Arkansas flag was reported captured along with, I believe, a 27th North Carolina Flag, A regiment that was brigaded with the 2nd Arkansas Battalion at the time.