By doing a Google Search for Arkansas Flat I found 2 references, and I am including a couple of links that I think will further help with location.
This first entry is an excerpt from a family history.
Beuford and Virgie McGee Family by Mrs. Virgie McGee BEUFORD HINTON MCGEE born Sept. 26, 1912 at Macomb, Oklahoma, died March 4, 1977 at Vernon, Texas, buried at Memory Garden Cemetery at Pampa, Texas. Married VIRGIE LEE RAY Sept. 23, 1937; lived in Tecumseh where Beuford drove a bus for the Shawenee-Tecumseh Bus System and Virgie taught school. Virgie also taught at Arkansas Flat and the Black School System before moving to Skellytown, Texas.
This 2nd entry is from a link in which the person was responding to a question about an Isenhower family.I think the message was dated 1999.
"Robert, I did a lookup in the Pottawatomie County OK History book for you. There is a Daniel Isenhower on page 62. He is the only Isenhower listed in the index. On page 62 the article is titled "History of Arkansas Flat School And Brown Community. It was written by Mrs. Ida McBride White who moved there in 1891 and died Dec 23, 1981. The article is a brief history of Arkansas Flat School and Community as remembered by a pioneer who came to the community as a small child and grew up with the community. The very earliest settlers who made the run into this strip whick was opened for settlement September 22, 1891 were:
many names before Isenhower,
... "Daniel Isenhower, (Mrs. Isenhower will be remembered as the first lady to vote in this pecient.) She died in 1926 at 83 years."
many names after Isenhower.
It goes on to say Brown, a small village in the community, seven miles west of Tecumseh, on #0 Highway had a post office in the early days where people for several miles around went for mail addressed to "Brown, Oklahoma Territory". (End of articles)
In looking at the 1920 Pottawatomie Co. census I found that the above Daniel Isenhower was on the same page as a Charles Jett family, from MO, so if this was your Jett family they were definitely in the same community.
There is more than one history of Pottawatomie County.The short history published in 1936 is online through my library ID card access and I did not find the story referrred to above in that history, so it must be in one published about 1987.
This next link is to the Pottawatomie County Oklahoma Genealogy Club site.Under Ghost Towns there is a short History of Brown.You might want to look into contacting or visiting their library.Hours and days can be found, cost, etc. through this site.I have not visited this site, personally.