Slice the chicken breasts into 2–3 inch long strips about 1/2–1 inch wide using a knife or kitchen shears.
In a large bowl whisk together hot sauce, melted butter, paprika, garlic powder, light brown sugar, chilli flakes, thyme (if using), salt and pepper to make the buffalo sauce.
Add the chicken strips to the bowl and toss to coat completely; marinate for at least 15 minutes or up to 4 hours in the refrigerator.
Heat a heavy-duty large skillet over medium-high heat. Add the chicken and all of the sauce to the hot pan.
Cook, stirring frequently, for 8–10 minutes until the chicken is opaque and cooked through and the sauce has reduced but remains saucy; remove from heat and let cool slightly.
Prepare the remaining toppings: shred lettuce, shred carrots, dice celery, slice scallions, shred cheddar and slice avocados.
To assemble each wrap, lay a tortilla flat and spread about 2 tablespoons of blue cheese dressing along the center.
Layer lettuce, shredded carrots, diced celery, sliced scallions, a generous portion of buffalo chicken, shredded cheddar and sliced avocado over the blue cheese in that order.
Fold the side of the tortilla closest to you over the filling, then fold one side inward and the other side inward, and finally roll away from you to form a tight seal with the seam on the bottom.
Slice the wrap in half if desired and serve immediately.