Ken,
I believe that I found the information in one of the old Lawrence County, apparently one that I do not have a copy for, as I have reviewed the issues that I have. I contacted Greg a few years ago in regards to the Flag presented to Thomas Churchill, and in my research, found the short mention of the flag being presented to the men. It did not specifically state the unit, but the family member for whom the writer was connected was in the 1st Arkansas Mounted Rifles from Lawrence County, which would have been Company E.
It is interesting to note in the Lawrence County Historical Quarterly Volume 7 Issue #3 Summer 1984 in a story regarding the school in Smithville the story of a Union Unit passing through Smithviile on the Hookrum (Evening Shade Road). According to eyewitness J. N. Barnett (a student at the school) he saw:
"Officers riding the finest horses he ever saw in his lifetime. They (union soldiers) carried many flags and banners, had decorated bridles, saddles and the saddle
blankets almost covered the horses. They had military emblems on their uniforms and hats. Following the calvacade were many wagons loaded with supplies." The unit was not recorded, bur given that it apparently was the first time Federal troops passed through Smithville, it would have been early in the War. Probably 1862. I know the 5th Illinois Calvary was in the vicinity about the time this would have occurred. I would guess the banners would have been the guidons and the flages the Regimental and National Colors?