A blue military flag with a state coat of arms in the center is very much in the tradition of state militias so if this is what Cleburne got as commander of an Arkansas state troops regiment I would not be surprised so long as other flags of this style are also mentioned in period documents, newspapers, etc.
To be honest I have only done a couple Arkansas newspapers of the era and all of the period Memphis papers but other than this flag I do not recall any other flags of this style being mentioned.
Greg Biggs