Preheat oven to 375°F (190°C).
In a large bowl, mix together cream cheese, sour cream, mayonnaise, garlic, parsley, salt, black pepper, and red pepper flakes until well combined.
Stir in mozzarella and cheddar cheeses.
Transfer the mixture to a baking dish and spread evenly.
Bake for 20–25 minutes or until hot and bubbly.
Serve warm with chunks of French bread for dipping.