Preheat oven to 325 degrees.
In a large bowl combine the grated cheeses and the green chilies. Turn into a well-greased shallow 2-quart casserole (12x8x2").
In a large bowl beat egg whites just until stiff peaks form when beater is lifted.
In a small bowl combine egg yolks, milk, flour, salt and pepper. Mix until well blended.
Gently fold beaten egg whites into egg yolk mixture.
Pour egg mixture over cheese mixture in casserole. With a fork, ooze it through the cheese.
Bake 30 minutes. Remove it from the oven and arrange tomato slices, overlapping, around edge of casserole.
Bake 30 minutes longer or until brown.