Kingman is not between Nashville and Flagstaff.
I just drove our motorhome with tow car on I-40 from Nashville to Flagstaff a week ago. No problem at all. Some areas have been repaved, so not as bad as used to be. Was quite a pleasant and easy drive. Wind can be a problem though, so check the weather.
By far, the worst part of my trip was on I-17 between Flagstaff and Sedona. Now that rattled my fillings!
We stayed at Walmarts along the way, as well as Rockwell RV Park in Oklahoma City and USA RV Park (as kalynzoo mentioned) in Gallup NM. Both good and easy stops.
2002 Itasca Suncruiser 32V
2012 Suzuki Grand Vitara