Preheat oven to 300 degrees, Layer 1/3 diced chiles in the bottom of a 4-quart baking dish. cover these with a layer of cheddar cheese. Layer in another 1/3 of the green chiles. Cover this with a layer of Jack cheese. Layer in the last of the green chiles.
Separate the eggs. Beat the yolks then add the evaporated milk, flour, salt and pepper. Mix well.
In a separate bowl, beat the egg whites until stiff. Fold the whites into the yolk mixture and pour over the layered chile/cheese mixture. Bake for 2 hours, uncovered. Pour enchilada sauce over the top and bake for an additional 30 minutes.