Heat 1/4 cup extra virgin olive oil and the red pepper flakes in a large skillet over medium-low heat; cook gently for about 3 minutes to infuse the oil.
Remove the pan from the heat and stir in the crushed or minced garlic; cook in the warm oil for about 20 seconds, then add the crushed tomatoes.
Stir in 1 teaspoon sugar and 1/2 teaspoon salt, then simmer the sauce on low for 20 minutes, stirring occasionally.
While the sauce simmers, prepare the chicken: pat the breasts dry and slice each breast horizontally to make two fillets if desired.
Cover the fillets with plastic wrap or parchment and gently pound thicker areas to an even thickness using a meat mallet or the base of a heavy skillet.
Season the chicken with 1 teaspoon salt and 1/2 teaspoon black pepper.
Heat 2 tablespoons olive oil in a heavy skillet over medium-high heat until shimmering, then add the chicken fillets and cook 3–4 minutes per side until golden and cooked through.
Transfer cooked chicken to a plate, tent with foil, and keep warm.
Bring a large pot of water to a boil, add 1 tablespoon salt, then cook the rigatoni for 1 minute less than the package instructions.
Reserve 1 cup of the pasta cooking water, then drain the pasta.
Add the drained rigatoni to the sauce with 1/4 cup of the reserved pasta water and toss over low heat until the pasta is fully coated, adding more cooking water if the sauce becomes too dry.
Toss in the packed cup of baby spinach and stir until wilted and evenly distributed through the pasta.
Check seasoning and adjust salt and pepper to taste, then top the pasta with the cooked chicken and garnish with fresh parsley, grated parmesan, and a drizzle of extra virgin olive oil before serving.