If you want to follow up on this Robert Lynn McLin, here are some pointers:
Robert Lynn McLin born PA Dec. 1756(?). Served PA forces and NJ Line (Rev. War, PA Archives and Records; U S Pension Office).
John Sevier’s journal 1793-1813 refers to Robert Lynn McLin as “colonel” under Brig Gen. Sevier in Expedition against the Cherokees and Creeks [War of 1812]
I found the settlement of his estate in Washington County, Tennessee Settlements of Estates, 1790-1867, compiled by Rev. Silas Emmett Lucas, Jr., and Ella Sheffield. McClung Collection number 62584, East Tennessee Historical Center, Knoxville, TN
These records, I know, belong to the older Robert Lynn, not to Alexander's son, Robert Lynn (who would have been too young to earn these mil credits and died at least 25 years later than this R.L.) but be aware that in Washington County until about 1832, there were two Robert Lynn McLins.
The other pointer that I would offer is that about the time R.L. died, they had opened up southern areas of TN to white settlement. Since I couldn't find Thomas in Washington County after 1832, try censuses or Goodspeed's Histories for McMinn and Blount, where I know other McLin relatives went. The area these McLins lived in was near the border with Greene county. I've found several relatives in Greene County, but I didn't think to look for Thomas there.You can safely ignore Lincoln and Franklin counties. I did a lot of research in those counties for this time frame, because two of Alexander's sons went there. and I looked for other relatives but didn't find any. I would have noticed if I ran across Thomas' name.
I never sent off for R.L.'s military records, but they might prove very helpful to you. The application for Rev. War pension, at least, typically names the wife and sometimes the children. If you do send off for them and they happen to mention Alexander as his brother, please let me know.