Preheat oven to 375 degrees F (190 degrees C).

Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain and set aside.

Heat the oil in a large deep skillet over medium-high heat. Add chicken, and cook until firm and lightly browned, about 5 minutes. Stir in the bell pepper and chorizo and cook for 5 minutes until the chorizo is hot and the chicken is no longer pink in the center. Remove from heat.

Pour the tomato puree, cream, and red pepper flakes into a small saucepan. Bring to a simmer over medium-high heat, then reduce heat to medium-low, and simmer 5 minutes until the sauce has thickened. Add drained pasta and sauce to the skillet containing the chicken and mix well. Spoon the mixture into an oven proof dish. Sprinkle the Cheddar, mozzarella, and Parmesan cheese over the top. Bake 30 minutes, or until the top is golden and bubbly.