Bob, the situation was just the opposite. They first served in the 7th Kentucky Mounted Infantry and were later transferred to the 13th Arkansas Infantry.

Capt. R. C. Flournoy's company was organized at Napoleon, Desha County, Arkansas, and traveled to Camp Burnett, near Clinton, Kentucky, where it was mustered into service as (old) Company K, 7th Kentucky Mounted Infantry. I don't know why they joined a Kentucky regiment; but it may have been due to the fact that most of the officers and many of the men were recent immigrants from Kentucky, and had strong ties to that State. At any rate, Flournoy's company was transferred to the 13th Arkansas Infantry on April 13, 1862, following the battle of Shiloh, and was designated as (new) Company E.

The 13th Arkansas, by the way, was down one company because (old) Company F had been transferred to the 5th Arkansas Infantry. Getting Flournoy's company put the regiment back up to ten companies.