In a large mixing bowl, combine the cooked chicken breast, buffalo sauce, mayonnaise, Greek yogurt (if using), chopped celery, red onion, and fresh parsley. Mix until well combined.
Season the buffalo chicken salad with salt and pepper to taste. Adjust the amount of buffalo sauce according to your desired level of spiciness.
To assemble the wraps, lay out the flour tortillas or wraps on a clean work surface. Divide the shredded lettuce evenly among the tortillas, spreading it out in a line down the center of each wrap.
Spoon the buffalo chicken salad mixture evenly over the lettuce on each wrap.
Top the buffalo chicken salad with shredded carrots and crumbled blue cheese, if desired.
Drizzle ranch or blue cheese dressing over the filling, if desired, for added flavor and creaminess.
To fold the wraps, fold in the sides of each tortilla, then roll it up tightly from the bottom, enclosing the filling.
Serve the Buffalo Chicken Salad Wraps immediately, or wrap them tightly in foil or parchment paper for an easy grab-and-go meal.