Cut chicken breast into cubes. Cook in a skillet over medium heat until cooked through. Remove chicken from skillet.
Melt 2 tbsp of butter in the microwave. Pour into a medium bowl. Add 3 tbsp of hot sauce. Add the chicken to the bowl and toss to coat all of the chicken.
In a different medium skillet, add a pat of butter. When it has melted, add one of the flour tortillas. Top the tortillas with 1/2 cup of shredded cheese, as much of the buffalo chicken as you'd like, and another 1/2 cup of shredded cheese. Let the cheese melt for a few minutes. Top with the other flour tortilla. Butter the top tortillas as the quesadilla is cooking. Flip the quesadilla to cook the other side. Make sure the cheese is melted. Once it is melted, remove it from the heat and transfer to a cutting board. When slightly cooled, cut into triangles.