Preheat oven to 350 degrees F. Coat a 9×13 baking dish with cooking spray and set aside. Line a baking sheet with aluminum foil and coat with cooking spray; set aside.
Place the chicken in the prepared baking dish and bake in preheated oven for 20-25 minutes, or until juices run clear and meat is cooked through. Let chicken cool and shred. In a large bowl, combine shredded chicken and buffalo sauce; mix well. Increase oven temperature to 400 degrees F.
Lightly flour a work surface and rolling pin; roll pizza dough into a 14×10-inch rectangle. Spread with chicken-sauce mixture, leaving a 1-inch border around the dough edges on all sides. Top mixture with blue cheese crumbles and mozzarella cheese.
Fold 1 inch of dough over the filling on the short sides of the rectangle. Fold the long ends over the filling, pinching the dough together at the corners. Roll the dough, starting at one of the long ends, as tightly as possible. Pinch the seam to seal.
Transfer the roll, seam side down, to the prepared baking sheet and brush with the egg. Bake for 30 minutes, or until the bread is golden. Loosen the bottom of stromboli from the foil with a spatula; transfer to a cutting board and let cool. Cut into slices and serve warm.