Preheat your oven to 350°F. Grease a 9x13-inch baking dish with olive oil.
In a large mixing bowl, combine the softened cream cheese, sour cream, garlic powder, onion powder, salt, black pepper, and red pepper flakes. Mix until smooth and well combined.
Add the shredded chicken, chopped spinach, cooked rice, half of the mozzarella cheese, and half of the Parmesan cheese to the bowl. Stir until all ingredients are evenly coated with the cream cheese mixture.
Transfer the mixture to the prepared baking dish, spreading it out evenly. Top with the remaining mozzarella and Parmesan cheeses.
Bake in the preheated oven for 25-30 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let it cool for 5 minutes before serving.