Cook chicken tenders according to directions on package, then cut into bite-sized pieces. Set aside.
In a large pot, heat oil over medium heat. Add onion and cook until tender (about 6 minutes). Add garlic and cook until fragrant, about 1 minute more. Stir in tomato paste and crushed red pepper flakes.
Add diced tomatoes and chicken broth and bring to a simmer. Let cook for 5-6 minutes.
Add pasta and cook 6-8 minutes more, or until pasta is al dente.
Right before serving, mix in cooked chicken, Parmesan and mozzarella until just melted and season generously with salt and pepper.