Preheat oven to 375°F. Lightly grease a 9×13-inch baking dish with olive oil.
Boil manicotti in salted water until very al dente, 6–7 minutes. Drain and cool on a lightly oiled sheet.
Stir Alfredo sauce with milk in a bowl until smooth. Spread about 3/4 cup in the baking dish.
Combine ricotta, 1 1/2 cups mozzarella, 1/2 cup Parmesan, chicken, garlic, Italian seasoning, salt, pepper, and 1 tbsp parsley.
Spoon or pipe the filling into each manicotti shell.
Nestle stuffed shells in the dish. Pour remaining Alfredo over the top and spread evenly.
Scatter remaining mozzarella and Parmesan over the sauce. Cover the dish tightly with foil.
Bake 20 minutes. Uncover and bake 12–15 minutes more, until bubbling and lightly browned.
Rest 10 minutes. Sprinkle remaining parsley and a pinch of red pepper flakes, if using. Serve warm.