I'm not related, but met someone with the name Fryrear and thought it would be interesting to track down.
Turns out the Fryrear I met is son of Cecil Andrew Fryrear Jr. and hence, great grandson of your Finley F. Fryrear. I dug around trying to locate Finley - found him in 1910 and 1930 Tuttle, Grady Co., OK and he and his wife Fannie are also buried in Fairview Cemetery in Tuttle. Finley ranged in birth year estimates of 1863 (tombstone) to 1866 (1930 census ) and possibly even 1870 (1910 census but difficult to read age).
I searched all over Kentucky and elsewhere for a Fryrear matching Finley in 1870 and 1880 etc. but with no luck. Then I stumbled over a Finley Fishback age 5 KY in 1870 Grant Co., KY. The apparent father is Wm, age 30 KY (an initial also but unclear) and apparent mother Harriet F(?). age 27 KY. In the household was a John Finley, age 38 and family.
So...a fry is a fish, and rear and back are synonymous. Perhaps y'all's Finley changed his name?