The flag of the First Arkansas was presented to the State of Arkansas in front of a joint session of the General Assembly on May 27, 1865. If you can get to a library that has old issues of the Washington County Historical Society's "Flashback" publication, a detailed description of the ceremony, as reported in a Little Rock newspaper, is at vol. 14, no. 1, pp. 19-20. It does contain some hints about the flag, reflected in the messages and speeches which surrounded the ceremony. These state that the flag had engagements inscribed upon it, and an article in the same newspaper suggests that the engagements were:

Newtonia, Mo., Sept. 15, 1862
Newtonia, Mo., Oct. 13, 1862
Yokum Creek, Ark., Nov. 15, 1862
Prairie Grove, Ark., Dec. 7, 1862
White Oak, Ark., Feb. 3, 1863
Fayetteville, Ark., April 18, 1863
Enterprise, Mo., Sept. 15, 1863
Cross Timbers, Mo., Oct. 15, 1863
Buffalo Mountain, Ark., Nov. 9, 1863
Kingston, Ark., Nov. 10, 1863
Sugar Loaf Mountain, Ark., Dec. 23, 1863
Richland, Ark., Dec. 25, 1863
Nubbin Ridge, Ark., Oct. 20, 1863
Fayetteville, Ark., Oct. 28, 1863
Fayetteville, Ark., Nov. 3, 1864.

The flag of the 2nd Arkansas was also presented to the State. A search conducted in the early 1960s by Prof. Lemke of the WCHS and Dr. Ferguson of the Arkansas Historical Commission revealed that these flags are no longer to be found in the state archives.