This is much further west... The Salt Fork of the Arkansas flows into the Arkansas just south of Ponca City OK at least 50 miles northwest of Yale.

Capt Boone was mistaken. They had diverged from the north bank of the Arkansas for a few miles and completely missed the mouth of Cimarron (Red Fork). They marched all the way to Kay & Noble Co.s (OK) and found the Salt Fork and thought it was the Red Fork (Cimarron). The Salt Fork comes through the Great Salt Plains, sometimes called the Grand Saline, about 60 miles west of Ponca City. I don't remember but I think Boone figured out his mistake on his way back when he crossed both the Salt Fork and the Cimarron (Red Fork) to get to the Canadian R. -- Boone's Journal is online on the Chronicles of Oklahoma site.

Johnston is saying the Osage call it the Little Arkansas but Boone (erroneously but Johnston apparently didn't know it) called it the Red Fork. In the early 1800s, the Cimarron was known way out west and the mouth of the Red Fork of the Arkansas was known but white men didn't know they were the same river.

The Osage, Creek, Cherokee, and Plains Tribes crossed this area frequently and Boone mentions large Osage trails running north-south that he crossed on his trek west. However, traffic by whites was generally up the "Little Verdigris" (now named the Caney) into Kansas. Very few followed the Arkansas or Cimarron across Oklahoma -- there didn't seem to be a good reason to do so. The Cherokee Trail to California crossed the Verdigris at Coodey's Bluff (near present Nowata OK) and then northwest into Kansas and on through Colorado. The southern route west crossed the Choctaw Nation into Texas. The Cross Timbers and poor water probably had a lot to do with this. Going around the Staked Plains (Texas Panhandle) was probably a consideration to. If you were going from Ft Smith AR to Santa Fe, I think you'd go up toward present Claremore OK on the Verdigris and follow Black Bear's (Osage) Trail up the Caney into Kansas and connect with the Santa Fe Trail.

Bottom-line: I don't think Boone or Johnston or Cooper had a very good idea of where they were... EXCEPT Johnston had astronomers and surveyors with him. Black Beaver had to lead Col Emory from Ft Arbuckle to Ft Leavenworth in 1861 'cause even Emory didn't know the way and the maps were incomplete for that region.