Sam, I'm not from Buffalo County but live in central Nebraska and since no one has responded so far I'll give it a shot.
The Omaha-Ft. Kearney Military Road was just that, a road from "civilization" along the Missouri River to a U.S. Army outpost southeast of what is know Kearney, NE. The same route was part of what is elsewhere known as the Overland Trail, Mormon Trail, etc.
Most of the route is now farmed as the roads were eventually made to follow section lines although remnants do remain. I know of segments in Merrick and Hall Counties and presume there are probably some in Buffalo County. I can't help you beyond assuming any address on this route in the 1920's would be east or southeast of Kearney and probably on the north side of the Platte River but near to it, most likely in the vicinity of Shelton or Gibbon.