That drive is about 2250 miles, which can be done easily in five 450 mile days. If you drive the speed limit, don't encounter significant delays, and make "normal" 15 minute rest and fuel stops, this will have you on the road for about 8 hours a day, not including your lunch stop.
Breaking it into 5 equal days, overnights should be Flagstaff, Santa Rosa, OKC/Tulsa, and STL. Recommend you stay on the east side of the larger cities to avoid morning rush hour.