I'm not aware of any steam mills in IT. Lynch's Mill on Spavinaw Creek was built by Mormons on their way to Utah Territory. This was about where the town of Spavinaw is now. The area north of this is Lynch's Prairie -- mistranscribed in David Haimerl's book on Clarkson's Battalion as 'Finch's Prairie'. I have found no mention of the mill in period records.
Watie's Mill was (I believe) near the mouth of Brush Creek above Spavinaw Creek. I need to confirm this location. I've read it was both sawmill and gristmill.
There was a livestock-powered gristmill at Dwight Mission, a few miles north of present Salisaw. Park's Day Book mentions sending wagons from Webbers Falls to Dwight Mission for flour. I haven't found mention of other livestock-powered mills in IT though it seems they could be common being cheap to build and operate with, perhaps, "homemade" millstones.
Nail's Mill was on Blue River (creek) near Ft McCulloch and Nail's Bridge on the Texas Road. Winchester Colbert, Chickasaw Principal Chief, had a mill which I think was on Mill Creek north of Tishimingo.
As you well know, Phillips used Rhea's Mill in Arkansas a few miles northwest of Prairie Grove. This was a steam mill. There was also Dutch Mill AR north of Van Buren (formerly called Dutchtown). Blunt may have been using Dutch Mill before Prairie Grove. During the Prairie Grove campaign, Watie was sent to 'save' Dutch Mill and found Union cavalry had just left there.
Lt Col Thomas Fox Taylor had a mill which I think just burned a few years ago. I don't recall the exact location -- somewhere in the vicinity of Park Hill. (You'd think I know more about this one since he was an ancestor of mine!)
I think there was a mill on Boggy near Boggy Depot but it may have been post-war.
There may have been more than one mill near Ft Smith. I think Page's Mill was on or near Poteau River south of Ft Smith near present Pocola OK. Seems there was another mill not far south of the fort -- I think there is a Mill Creek that empties into the Poteau River south of the fort near present Arkoma OK.
I'm sure you know the Indian families ground their own wheat and corn by hand except for the few with large farms who sold their excess. It seems every populated area, mission school, or the like would have some kind of mill -- whether livestock or water-powered -- though I find no mention other than the above.
I'll search for my old notes and see if I have more or better info.
Ken