I'm also searching for death/burial information for Burnice/Burness McKinney, as well as records of his service, and the pension received by Elizabeth Cogdale/Cogdell McKinney. Her pension states that Burnice died on 23 Sep 1863.
Your post on Find-a-Grave notes his enlistment date as 15 Apr 1863; are you aware of any documentation of his enlistment? Two miscellaneous cards in the Compiled Service Records show that a B.M. McKinney of the 34th North Carolina Reg't was admitted to a Petersburg, VA military hospital in June 1864, and subsequently transferred to Richmond -- but there's nothing more in the NARA files.
Would be grateful for any data you're willing to share. Thank you!