Although I am not a Burnett descendant, I was born in Burkburnett in 1940.
Burkburnett was indeed named after Burk Burnett, the legendary owner of the 4 Sixes ranch, because he helped start the town.
The story is that he won his ranch in a poker game with a poker hand of 4 Sixes & named the ranch after that poker hand. The ranch brand is "6666".
President Teddy Roosevelt came to north Texas to hunt wolves with Burk Burnett, W. T. Waggoner & other ranchers in the area. They would also cross over the Red River into the Big Pasture area near Grandfield, Oklahoma & hunt wolves with Comanche Chief Quannah Parker.
During the oil boom of the 1910's & 20's, there were so many oil rigs that you could walk for a mile or so without touching the ground because the rigs were so close together. You could just step from one rig floor to the next one. Burkburnett is called "Boomtown".
The movie "Boomtown" starring Clark Gable & Spencer Tracy was loosely based on this period.