Carolyn Ellertson,
Since your "W. H. Fleming" enrolled in a Red River County, Texas militia in June 1861, he must have lived there. ..Did you find him on any census? ..Why was he there?
Below are my "Fleming" entries in my 128-page Name Index. If I were you, I'd track down the "James T. Fleming" found in the same "Savannah, Texas" militia as your "Wm. H. Fleming." The "P.A. Fleming" was in a militia that enrolled on Pine Creek and Red River, 24 miles east of the Lamar County line, which is a few miles from Savannah.
FLEMING
B. M. (Sgt, Titus Co, TST), A-86
E. H. (Hunt Co, TST), A-155
G. W. (Col, TST), 125, A-171, A-172
J. Crosby (Hopkins Co, TST), A-118
James T. (Red River Co, TST), A-64
Mary C. (1846 Fannin Co TX), 13
P. A. (Red River Co, TST), A-72
R. C. (Johnson Co TX), A-220
Wm. H. (Red River Co, TST), A-64
My Amelia E. (Fleming) Graves family (of Red River County) records simply show that she had a brother "Major Fleming, killed in Civil War" which sounds as though they had lost touch with him since no first name was given. It follows that he may not have been a "major" and may not have died in the Civil War. ...Notice that Amelia had a brother "James Fleming that died before 1914."
Please let me know your findings.
Patti, prochette@Juno.com