I found Richard in two places. The Civil War Soldiers and Sailors System lists him as a Private in Company B, 1st Arkansas Infantry Regiment.
He also appears in the Arkansas Civil War Soldier’s Index as a member of Company B, 1st Arkansas. This source places him in Cleburne’s 1st/Josey’s 15th
http://www.researchonline.net/arcw/index/index84.htm
The same information appears on Ancestry.com, which is a subscription service.
This information might have come from a pension application. According to Ingmire, there was no Richard Henderson that applied from Arkansas, but he might have applied from another state.