I have not found any evidence that implies the battle was in the vicinity of Atoka. There is no mention of the well known Texas Road or Butterfield Route and no mention of the well known stations along that route. Phillips states later that his plan was to neutralize the Creek, Seminole, and Chickasaw and then return in the spring to invade the Choctaw Nation.
The locations/movements in Phillips' reports cannot be reconciled with the Atoka vicinity. Specifically, he camped on the battlefield (Camp Kansas) and then moved 20 miles south to Camp Kagi/Kahi from which he wrote that he had been to Gov. Colbert's home. Had he been 20 miles south or southwest of Atoka, he would have been south of Boggy Depot which he apparently was not, based on both Union and Confederate reports. Gov. Colbert was Governor (i.e., Principal Chief) of the Chickasaw Nation where his residence was reportedly located. Atoka is, of course, well east of the boundary in the Choctaw Nation.
I haven't had time to digest everything in John Russell's posts though he clearly did his home work. The Phillips and Lehigh area seem plausable though my opinion is the battle was further north and west. I'm hoping Ralph Jones will provide some input also. He told me he had visited a possible site in the past (in Coal or Pontotoc Co., if I remember right).
I must state that I have no confidence in information from Mr. Jerry Coffee. His stories, by his own admission, were based on fragments of family lore which he embellished with his knowledge of the area to make them sound credible.