Preheat oven on broiler setting. Roast chiles under broiler on cookie sheet until skin is brown and charred on all sides. Cool until you are able to touch peppers, then peel off skin. Make a slit down one side of the pepper, and remove stem and seeds. Reduce oven temperature to 350 degrees F (175 degrees C).
Line the bottom of an 11 inch square baking dish with chiles. Layer Monterey Jack cheese and Cheddar cheese evenly over chilies. Spread cooked chicken over cheese. In a medium bowl, using a wire whisk, mix flour with a small amount of evaporated milk until it forms a smooth paste, then whisk in remaining milk and sour cream. Beat in eggs, one at a time. Pour evenly over chicken.
Bake in preheated oven for 40 minutes, or until center of pie becomes firm. Spread salsa over top, and bake for 15 minutes. Allow to cool 10 minutes before serving.
