Preheat the oven to 350°F (175°C) and spray a 9x13-inch baking dish with cooking spray.
Cook the rigatoni in salted boiling water according to package directions until al dente, then drain and set aside.
Meanwhile, melt the butter in a large skillet over medium heat. Add the diced onion and cook until softened, about 4–5 minutes.
Add the chive-and-onion cream cheese and heavy cream to the skillet, stirring until the cream cheese melts and forms a smooth sauce.
Stir in the salt, pepper, and crushed red pepper flakes, then add the drained diced tomatoes, squeezed spinach, and diced cooked chicken. Remove from heat.
Toss the cooked pasta into the skillet with the sauce, then stir in half of the mozzarella and half of the Parmesan until combined.
Transfer the pasta mixture to the prepared baking dish and sprinkle the remaining mozzarella and Parmesan over the top.
Bake for 20 minutes, until the cheese is melted and the dish is heated through. Let rest a few minutes before serving.
