Preheat oven to 425 degrees Fahrenheit and prepare a sheet pan by lining it with foil and spraying it lightly with pan spray. Set aside.
Soften 4 ounces cream cheese in the microwave for about 15-20 seconds. Add the softened cream cheese, 2 cups cooked shredded chicken, ¼ cup buffalo sauce, ¼ cup ranch dressing, ½ cup shredded monterey jack cheese, ½ cup bleu cheese crumbles, and 2 tablespoons sliced green onions to a large mixing bowl and mix until thoroughly combined.
Add about 3 tablespoons of the chicken mixture about 1 inch from the edge of 1 of the 10 small flour tortillas. Roll it up and place it seam-side down on the sheet pan. Repeat with each tortilla and place about 1 inch apart, not touching each other on the sheet pan.
Bake for 15-20 minutes or until the tortilla is lightly browning around the edges. Serve with sour cream, ranch, or your favorite dipping sauce!