Note: I am not related to the Fleming family, but am related to the Pabst family.
This is probably more than you wanted to know -- but the George Monroe Fleming you mention is may be a descendant of Enoch Monroe Fleming, b. KY 1816 who married 1st Wilhelmina Pabst. They had one son, James W. Fleming, b. 1848. Wilhelmina died bef 1870 .
Enoch Monroe Fleming then married 1871 in Richland Parish Elizabeth Cade (nee Perry). They had 2 sons -- George Monroe Fleming, b. ABT 1874 and Thomas Jefferson Fleming, b. ABT 1876. I don't have any further info on these two brothers. The use of the name Monroe suggests a relationship. Enoch Monroe Fleming died 14 January 1877.
Elizabeth married Dr. W. H. Berry in 1878. The 1880 West Carroll census enumerator used ditto marks under the name Berry for the two Fleming children.
Beware, if you search for the Fleming in that area of Louisiana that there were three unrelated Fleming families there before 1850.