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; drain and set aside.
While the pasta cooks, melt the butter in a large skillet over medium heat. Add the diced onion and cook until soft and translucent, about 5 minutes.
Add the chive-and-onion cream cheese and heavy cream to the skillet and stir until the cream cheese is melted and the sauce is smooth.
Stir in the salt, pepper, crushed red pepper flakes, drained diced tomatoes, thawed squeezed spinach, and diced cooked chicken until evenly combined; remove from heat.
Toss the sauce mixture with the cooked rigatoni and half of the shredded mozzarella and half of the Parmesan cheese.
Transfer the pasta mixture to the prepared baking dish, sprinkle the remaining mozzarella and Parmesan evenly on top, and spread into an even layer.
Bake for 20 minutes, until the cheese is melted and bubbly. Let rest a few minutes before serving.