Eureka, this solves some of the problem. However, his tombstone records his service with the 2nd Tennessee Infantry. Still, his name does not appear on a roster in any Tennessee Federal unit.

"The former home (ca. 1854) of Union Col. William P. Kindrick, Jr., 2nd Tennessee Mounted Infantry, stands across North High Street. Kindrick was captured near Corinth, Mississippi while organizing the 3rd West Tennessee Cavalry. Confined in Libby Prison in Richmond, Virginia, he escaped with 108 other Federal officers in February 1864. He returned home to Waynesboro where he died the following month and was buried in the family garden behind the house."

http://www.lat34north.com/HistoricMarkersTN/MarkerDetail.cfm?KeyID=091-A05&MarkerTitle=Difficult%20Times%20~%20Waynesboro%20during%20the%20Civil%20War%20