A couple of points:
The term Red Legs was in use many months before the formation of the 15th Kansas. For example, the Dec 10, 1862 KC Journal of Commerce talks about the Red Legs being horse thieves centered in Leavenworth. A quick search against the OR, shows a Feb 1863 reference to the Red Legs by Gen. Ben Loan of Missouri in a letter to Gen. Samuel Curtis.
Castel in Civil War Kansas claimed that "In both personnel and character they [the Red Legs] were nearly identical with Jennison's old Jayhawkers, and their leader was Jennison's friend and lieutenant, George Hoyt."
Starr also talks about the formation of the Red Legs in Jennison's Jayhawkers and gives more and different detail than Castel.
That's not to say that someone didn't later conflate Red Legs and the 15th Kansas.