This seems too much of a coincidence to ignore. Phillips was a 'free soiler' in Kansas and camped a Kagi/Kahi was the 14th Kansas Cavalry (Willett's Battalion).
I think it is worth investigating whether this could be a Choctaw name (or other tribe of the area, such as Caddo)-- as I always assumed -- but the Kansas/John Brown connection seems very likely to me.
Ken