Lay the flatbread out on a cutting board and use a knife to spread the cheese wedges across the entire surface of the flatbread. Sprinkle the little carrot pieces across the surface and top with the chicken, leaving about an inch without toppings (but still spread with cheese) at one of the shorter, curved ends of the flatbread. Drizzle the wing sauce over the chicken and then follow with the blue cheese dressing. Spread the lettuce over the other toppings.

Beginning with one of the shorter, rounded ends of the flatbread (the one opposite from the end without toppings), begin to tightly roll the flatbread over the toppings to form a wrap, finishing by pressing the cheesy surface of the end without toppings to the side of the roll. Place the wrap seam side down and use a sharp knife to slice the wrap into 8 “pinwheel” slices. You may want to finish each pinwheel piece by sticking a sandwich pick (long toothpick) through it.