Tony
As a research historian of the Third Kentucky Infantry, CSA, I would first like to say that the unit was not mounted at this time, and further the Confederate Government never gave the an official name change, so it is just the Third Kentucky Infantry, CSA. As a US military veteran I do not accept the enemy of the Confederavy called them.
I have nothing from my research on the Third that tells anything about casualties, etc, in the battle of Raymond. I know the unit heped on the retreat, but all I have is post-war accounts that tell about them being there at the retreat.
Greg