Cook white rice according to package instructions and set aside.
Season the chicken breasts with salt and pepper.
Fill a wide plate or a bowl with flour, and coat the chicken breasts in flour on both sides.
Heat olive oil and butter in a large skillet over medium-high heat. Add chicken and cook until golden brown (about 4 minutes each side). Transfer to a plate and set aside.
In the same skillet, add more butter and olive oil if needed, and add minced garlic and cook for 30 seconds.
Add in chicken broth, heavy cream, and parmesan cheese, mix and simmer for a couple of minutes until smooth.
Add chili flakes, dried thyme, dried oregano, dried tomatoes, salt, and pepper; simmer until thickened (about 5 minutes).
Return chicken to skillet; stir until coated in sauce. Serve over cooked rice and garnish with fresh basil.