This is the only piece I could find tying him to the Civil War

Dr. Flinn had a guard that was paid by the Confederate States government.

http://news.rootsweb.com/th/read/DECAMP/2001-04/0987899962

…….

This would seem to indicate that he saw no CW service

125 Jesse Washington Flinn, son of John, son of Patrick, son of Laughlin, b. Sept 4, 1801 in Stokes Co., NC, d. Dec 13, 1873 in Greenbrier Township, Independence Co., Arkansas. m.1 Margaret Bowen (She was listed on marriage bond as Margaret Boon. Relatives confirm it-was Bowen.) on Feb 21, 1826, in Stokes Co., Nc. He m. 2, Nancy Smith, Feb. 26,1847 in McMinn Co., Tenn. He m.3 Margaret Abigail French on Sept.10, 1858 in Independence Co., Ark. She was a dau. of Alpheus French and Juliet Byrne .He was a doctor. After he m. Margaret, they lived in Guilford Co. until about 1831, when they moved to Madison Co., Ky., and then in 1839 they moved to McMinn Co., Tenn., where Margaret Died in 1844. He must have been m. to Nancy Smith for a short time, for he moved to Independence Co., Ark. in 1857 where he m. Margaret Abigail French. .He spent the rest of his life as a farmer and stock raiser, also practicing medicine to some extent. He had attended Baltimore College of Medicine, now The University of Maryland Medical School. He is buried in Alderbrook Cemetery; Desha, Ark.

http://freepages.genealogy.rootsweb.ancestry.com/~berta/fff6.pdf