Place rack in middle of oven. Set 10 inch cast-iron skillet on a rimmed baking sheet, place on rack, and preheat oven to 400°. Whisk flour, cornmeal, baking powder, and salt in a small bowl to combine. Lightly beat eggs in a medium bowl to blend; whisk in creamed corn, chiles, cheddar, and Monterey Jack.
Mix butter and sugar in a large bowl with a wooden spoon just until butter absorbs sugar but butter is still in small pieces. Add egg mixture and mix until just combined. Mix in dry ingredients until barely incorporated.
Remove skillet from oven and lightly coat with nonstick spray. Scrape in batter (it should sizzle on contact and stay slightly mounded in the center). Bake cornbread until top is golden brown and springs back when gently pressed, 35–45 minutes. Let cool 10 minutes before serving.