In looking over the pictures I do not think this flag is from the Civil War period. The color of the field os too dark for one - exiting McCown flags are much bluer in their fields.
I also do not like how the unit designation and battle honors are applied to the flag. Something like this would stand out much more on a real period flags which was the point.
The cloth does not look right to me either nor does the sewing. I would indeed get it to a textile conservator for examination to be sure.
The Arkansas flags captured at Helena are variants with St. George's cross on them but these have a red cross instead of white. These were found only in the Trans-Mississippi theater. One that survives is for the 37th Arkansas Infantry held by Iowa today.