From Tulsa to Flagstaff is a nice trip. If you have time try to go a little further. At least to Seligman. You get to drive through Williams, and the stretch of 66 from Ash Fork to Seligman is a great run. Seligman is a unique, and fun place to turn around. You forgot to mention the month you want to travel, so I'm going to guess September. And September is a wonderful time to travel Route 66. That is the month we always do our Route 66 adventures. Enjoy your trip, and take your time to stop and smell the roses.
Don't forget the Big Texan in Amarillo for an excellent steak, or Ann's Chicken Fry in Oklahoma City for one of the best chicken fried steaks I've eaten. There is a little place in Shamrock, TX called "The Roost", and I am told you will really enjoy the food. That is our next must stop on our trip this September. See the Ghost Town of Glen Rio on the New Mexico border. And plan a stay in the Blue Swallow Motel in Tucumcari, NM if the time is right. Kevin, and Nance (Owners) are some of the best people you will meet on Route 66.