I know quite a bit about the Tennessee Kellows as I am part of that group and have researched them quite a bit.They came into Tennessee by about 1820 and spread out a bit after that.By the late 1800's some were in Texas, some in Arkansas, but many (including my great grandparents) stayed in Tennessee and lived in rural West Tenn. between the towns of Trenton and Dyersburg.Part of the group remained in Middle Tenn. as well.After looking at all my records, I don't see a definite answer.
I do show a John Kellow and James Kellow, born in the 1840's in Middle TN.John was in Texas by the time cameras were around though and I'm not sure what happened to his brother James.Of course, your picture could be a generation later and I don't have any more on them.They also had a set of cousins in Middle TN who could be a generation earlier than your picture.
The West TN Kellows were definitely still around in TN at the turn of the century.I have listed a James R. Kellow and a John W. Kellow.If the middle initials are correct then I guess they're out.They were brothers and were born in the 1850's in West TN - they were much younger brothers of my great great grandfather.I don't have much on their families and their siblings families though (except for my line, which shows no "J.D." from that time frame), so they could have a "J.D." in their lines maybe.There was one brother in this family named Samuel who went to Arkansas by the 1890's, so maybe it was someone in his line as well.
So, I can't tell you for sure, but if your grandmother was in West TN early in the 1900's I can narrow it down to that family probably.
I doubt that I would even recognize anyone even if I saw the photo since I don't really have much in the way of photos from my Kellow side.If you have an electronic version, I'd love to see it and maybe someday I could figure it out!My e-mail is firstname.lastname@example.org if you have a scan.