I am forced to assume here because of lack of information within the article as to which 1st Arkansas Infantry Flag this was. I could suspect that it was the flag of the 1st Arkansas Infantry of African Decent which became the 46th U.S.C.T. in May of 1864.

Was the 1st ARK Inf (A.D.) part of Steele Army at Jenkins Ferry?

Or is this article talking about the flag of the all white 1st ARK Inf U.S.?

The article says that "Pete" was "attached" to the Headquarters and that his saving the regimental colors was some sort of extraordinary act. That most likely this Wagon being abandoned was the Headquarters gear. It doesn't say that "Pete" was a soldier. So I can see how this could have been the 1st Ark Inf. U.S. flag that had been abandoned.