I'm thrilled to hear someone else is interested in pursuing this. The link below includes quite a few reports from the ORs which give clues as to the location, some of which you may not be aware of, plus a couple of secondary sources at the bottom.
From the Report of the Adjutant General of the State of Kansas, 1861-1865. Vol. 1. located at http://skyways.lib.ks.us/genweb/archives/statewide/military/civilwar/adjutant/14/history.html comes the paragraph below. While it may give some clues, its accuracy is suspect as Willett's Battlion of the 14th was at Ft Gibson with Phillips, not under Brown at Ft Smith. Also, Phillips complained he never heard from the other battalion of the 14th -- he surely would have known had they reached North Fork Town where he left corn for them.
Just before this time, Col. Moonlight was relieved from the command of the regiment, Maj. J. G. Brown succeeding him. Under this officer the 14th Kansas marched during the month of February on an expeditioin into the beautiful but almost deserted Choctaw country. The line of its march was that of Lieutenant Whipple's survey for the Southern Pacific Railway via Sherman, Texas. Many of the iron bridges built by that pioneer of the Pacific Railroad, the Overland Mail Company, yet remained. The expedition was intended to penetrate to Boggy Depot, C. N., and was to co-operate with a force from Fort Gibson, C. N., under command of Col. Wm. A. Phillips. On account of orders received from Headquarters District of the Frontier, the entire regiment did not proceed further than North Fork Town, on the Canadian river, eight companies of the regiment returned to Fort Smith under Maj. Brown, and Cos. B, K, L and M accompanied Col. Phillips. As the only cavalry with the force it acted as the advance of teh command while penetrating the enemy's country, and when within twenty miles of Boggy Depot, it was found necessary to retreat to avoid a largely superior force, this battalion of cavalry acted as the rear guard of Col. Phillips' little army, doing signal service throughout.
There very well may have been an undocumented fight on the Texas Road near Muddy Boggy but I find no evidence it occurred in February 1864. The identified Civil War graves at Atoka are of Dawson's 19th Arkansas Infantry who were camped there in 1862.