Preheat the oven to 350°F (175°C) and spray a 9x13-inch baking dish with cooking spray.
Cook the rigatoni in a large pot of salted boiling water according to package directions until al dente, then drain in a colander.
While the pasta cooks, melt the butter in a large skillet over medium heat. Add the diced onion and sauté until soft and translucent, about 5 minutes.
Add the chive-and-onion cream cheese and the heavy cream to the skillet, stirring until the cream cheese melts and the sauce is smooth.
Stir in the salt, black pepper, crushed red pepper flakes, drained diced tomatoes, thawed squeezed spinach, and diced cooked chicken; cook just until heated through, then remove from heat.
Toss the cooked rigatoni with the sauce in the skillet (or in a large bowl), then stir in half of the mozzarella and half of the Parmesan until combined.
Transfer the pasta mixture to the prepared baking dish, sprinkle the remaining mozzarella and Parmesan evenly over the top.
Bake for 20 minutes, until the cheese is melted and bubbly. Let sit a few minutes before serving.