Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13-inch baking dish with cooking spray.
Lay half of the chilies evenly in bottom of baking dish. Sprinkle with half of the Jack and Cheddar cheeses, and cover with remaining chilies. In a bowl, mix together the eggs, milk, and flour, and pour over the top of the chilies.
Bake in the preheated oven for 25 minutes. Remove from oven, pour tomato sauce evenly over the top, and continue baking another 15 minutes. Sprinkle with remaining Jack and Cheddar cheeses, and serve.