With two forks, shred your cooked chicken (or roughly chop it with a knife), and place it into a large mixing bowl.
Add the shredded carrots, diced celery, and hot sauce to the chicken, then mix it thoroughly to distribute the veggies and coat everything evenly. Add more hot sauce if you'd like it to be a bit saucier and more intense; set the bowl aside.
Place the wrap down onto a flat surface and spoon about a tablespoon of blue cheese dressing onto the wrap, spreading it out evenly up to the middle of the wrap. Leave some room around the edges of the wrap for folding so that you don't have dressing leaking out of the wrap once its folded.
Lay down a handful of greens over the dressing, closer to the bottom half of the wrap (not quite centered), and top the greens with tomatoes and about a cup's worth of the Buffalo chicken mixture; a bit more if you think your wrap can handle it. Some wraps are flimsy, so be careful.
Sprinkle the blue cheese crumbles on top of the chicken.
To fold the wrap, fold the left and right sides halfway toward the middle. Fold the bottom part of the wrap up and over the contents of your wrap. Roll the wrap up and tuck your filling in as you roll. It's normal for things to slide around, and it may get messy, but that's ok.
Once wrapped, cut it in half and serve it with fries or a salad.