Perhaps this largest group of 'Loyal Creeks' et al was not headed to Kansas. One account says they were making an arc around Cooper's right flank to rendezvous with Cherokee allies -- likely McDaniel's Reserve Company (Drew's Regiment) of the Cooweescoowee District.
It seems possible that at least some of the Cherokee on the side of the Loyal Creeks in the battle were from McDaniel's Company. (Evan Jones' letter states he got his information from two Cherokee who were at the battle "at the bend of the Arkansas".) After the battle, Opothleyahola's band moved to and camped near James McDaniel's home -- as did all of Drew's Regiment, contrary to orders from Cooper.
It seems if they were headed to Kansas and Walnut Creek (Walnut River at Ark City KS?), they would have moved further away from Cooper after the battle instead of to the east generally closer to Cooper. Per my recollection, it seems this group didn't move toward the Arkansas River in Kansas until after Chusto Talasah (Caving Banks). The "Cox Map" shows their route and camp locations.
They undoubtedly knew their way. They had been to a council with Plains Tribes at the salt plains in western Oklahoma a couple of years before (per Annie Abel).