Pre-heat the oven to 400. Line a baking sheet with foil and then lightly mist it with cooking spray and set aside.
In a large skillet or sauté pan, bring the oil to medium-high heat. Add the chicken breasts in a single layer and cook for 3 minutes on one side, flip them over, and then continue to cook for 3 minutes on the other side. Add the Buffalo sauce to the pan and wait until it bubbles (should happen almost immediately. Lower the heat to medium-low and cover the pan. Simmer for about 15-20 minutes (depending on the thickness of your chicken breasts) until the chicken is fully cooked through.
Remove the lid from the pan and transfer each breast to a cutting board, shredding it using two forks and then returning it to the sauce. When all the breasts are shredded, stir them into the sauce until thoroughly combined. Continue to cook for 3-5 more minutes until the sauce thickens and soaks into the chicken. Transfer the chicken to a mixing bowl and add the cream cheese and blue cheese dressing. Stir together until cream cheese melts in and the ingredients are well combined.
Place about half the tortillas between two paper towels and microwave them for 30-60 seconds until they are warm and pliable. Place a tortilla on a clean, dry work surface and then scoop two tablespoons of chicken filling onto the bottom third of the tortilla. Roll the tortilla up from the bottom to surround the filling and once it’s rolled into a tube, place it on the prepared baking sheet, seam side down. Repeat steps with the remaining ingredients (including microwaving the other half of the tortillas when you get to them).
Place the baking sheet in the oven and bake for about 15 minutes until tortillas start to get golden and crispy.