I find no record of him in any Confederate unit.

Rodham Kenner Gibbs
Birth: 1834
Death: 1898
Pvt, Co. C, 2nd Brigade, Texas State Rangers

In Shelby County since 1846. Enlisted at Concord, TX. Served 1862-1865.

http://trees.ancestry.com/tree/9780726/person/-128667361/photo/bf9030bd-7400-46a6-b382-a0229a804993?usePUBJs=true

http://trees.ancestry.com/tree/9780726/person/-128667361/photo/fe48fd6c-e850-439f-80e4-28e741408028?usePUBJs=true
………

R Gibbs
in the Texas, Muster Roll Index Cards, 1838-1900

Name: R Gibbs
Enlistment Date: 6 Jan 1863
Enlistment Place: Concord
Record Type: Civil War Index- Abstracts of Muster Rolls

…..

R. Gibbs, Pvt.
W. T. Nettles, Capt. Co. C, 2nd Brig. BG Geo. W. Van Vleck Comdg. TST
Enlisted Jan. 6, 1863 at Concord, Texas for 3 months
Enl. at Camp Gentry, Concord, Tx. Jan. 24, 1863

Source Information
Ancestry.com. Texas, Muster Roll Index Cards, 1838-1900 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011.
Original data: Civil War Muster Rolls index Cards (both Confederate and Union). Also Texas State Rangers. Austin, Texas: Texas State Library and Archives Commission.

………

George W. Van Vleck of Woodville had been district clerk of Tyler County. He was born in New York in 1815. As a brigadier general, Van Vleck commanded the Second District, Texas State Troops, which included Chambers, Liberty, Polk, Tyler, Hardin, Jefferson, Newton, Jasper, and Orange counties.

https://books.google.com/books?id=AYXk0sNiix0C&pg=PA130&lpg=PA130&dq=Confederate+General+George+W.+Van+Vleck&source=bl&ots=1Qf5dMk3xI&sig=P1fcix8wmQK5MQValA79_fMeRKo&hl=en&sa=X&ved=0CCgQ6AEwAmoVChMImvS71_7kxgIVxjuICh3Bnwgi#v=onepage&q=Confederate%20General%20George%20W.%20Van%20Vleck&f=false

https://books.google.com/books?id=NaLzBgAAQBAJ&pg=PT98&lpg=PT98&dq=Confederate+General+George+W.+Van+Vleck&source=bl&ots=9sNCyg3MSx&sig=caxr24BJe87WV4rSZWQ4YpwdGNY&hl=en&sa=X&ved=0CB8Q6AEwAGoVChMImvS71_7kxgIVxjuICh3Bnwgi#v=onepage&q=Confederate%20General%20George%20W.%20Van%20Vleck&f=false

…….

R K Gibbs
in the Alabama, Texas and Virginia, Confederate Pensions, 1884-1958
Name: R K Gibbs
Birth Place: Shelby
Age: 65
Pension File Number: 04576
Application Type: Veteran

His pension application records he served in Company F. Huetts Company, Lane Reg. 1862 to 1865

Source Citation
Texas State Library and Archives Commission; Austin, Texas; Confederate Pension Applications, 1899-1975; Collection #: CPA16526; Roll #: 408; Roll Description: Pension File Nos. 03322 to 04620, Application Years 1899 to 1899