I have many sources for Flat Rock Creek. My Pecks book, taken from Pikes newpaper accounts tells that the hay operations extended over a great extent of the prairie that was north of Fort Gibson/Blunt, and west of the Nesho River. I tend to disagree with the actual location where you claim the battle was fought for two reasons. First I know several people who metal detect and have found civil war period bullits in the inlet running into the river.
Second in Pecks account as I recall it, he tells about the burial details picking up bodies and moving them to burry. If that in fact happened then the location you mentioned would not be the sight of the battle. Also the engagement was over a great distance, and the exact location of the revaine is most likly now under water.
Peck writes that even though he wasn't there when the attack happened, he did have his group of wagons with their teamsters in the area working on the hay, and as soon as those who excaped arrived at the Fort Peck went out looking for his group and found them totally unaware that an attack had happened at all. This tells me that the haying operations were indeed spread out.
As far as the route taken by the Confederates, I Have walked almost the complete route from the crossing of the arkansas river to the tall hill where they survaied the Union troops working in the fields, I used a pair of period binoculars so I could see it as they could have seens it.
It is interesting to note that I was able to identify the names of a son and father who fought in this engagment, and the son captured his father. The father was a member of the Kansas Cav. company, that was supposed to be providing protection, and the son was a member of Howell's Texas Battery.