Thanks Patti. Later maps of the area show Cochran's Academy in the Choctaw Nation on Middle Boggy, however, Cochran's was in the Chickasaw Nation on Clear Boggy. From this, I leap to the supposition that when Phillips was at Cochran's, he thought he was in the Choctaw Nation on Middle Boggy, per his map. I'm supposing that the Battle of Middle Boggy was actually on the head waters of Clear Boggy and that Camp Kagi (or Kahi) was about 20 miles south on the Blue.
As an aside, the reference in Mark of Heritage places this in the Choctaw Nation, which it was in 1844 but as you well know, after 1858-1859(?), it becomes the Chickasaw Nation when the Chickasaw separate from the Choctaw and reestablish their own government.