Confederate civil war records rarely reveal parentage. When they do it's pertaining to claiming receipt of a deceased's pay, accounts due, and his effects. Usually a parent or sibling, identified on an affidavite, usually showing residence.

In John Flemmings case, his records end with his death due to Chronic Diarrhoea at the Hart's Island, New York Harbor prison camp, June 8, 1865, having been captured at SSRR* April 2?**, 1865.

M311: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Alabama

* I have no idea what the abbreviation SSRR stands for.

** Difficult to discern on-line

Could be:

04 02 1865 The engagement at Sutherland's Station, on the South Side Railroad, the Richmond, Va. Campaign.
[The Chronological Tracking of the American Civil War, Ronald A. Mosocco]