Preheat oven to 400 degrees F (200 degrees C). Grease a 9x13-inch baking dish.
Split the chiles open, and spread half the chiles into the bottom of the prepared baking dish. Layer with the Cheddar cheese, and top with the rest of the canned chiles. Whisk together the eggs, flour, and evaporated milk in a bowl. Pour the mixture over the chiles and cheese.
Bake in the preheated oven until set, about 30 minutes; remove casserole, and top with the Monterey Jack cheese. Pour the green chili salsa over the top; return to oven, and bake until the cheese is melted, about 15 more minutes.
