We have made that trip numerous times. Check the weather forecast for Flagstaff, AZ since snow & cold weather is a good possibility. Wind will be your problem in NM, TX and Oklahoma. Tornado weather is common in that time period. Pay attention to weather forecasts.
The last couple years the campgrounds West of OK City were full of oil workers. Not sure if that is still the case.
Memphis has(d) a lot of road construction last year and it was mess going through there. Not sure if it is cleared up yet. Maybe someone on the Forum can tell what it is like now.
I-40 through TN is a great road and I-81 is great also. Lot of truck traffic on I-81 and some construction delays.
Have fun.