Cut the chicken into bite-sized pieces and season with paprika, garlic powder, and sea salt; set aside.
Bring a large pot of water to a rolling boil and generously season with salt.
Heat 1 tablespoon olive oil in a large skillet over high heat. Add the seasoned chicken and cook until browned and cooked through, about 4–5 minutes; remove chicken and set aside.
Reduce heat to medium and add the remaining 1 tablespoon olive oil and 1 tablespoon butter to the same skillet. Add the diced onion, minced garlic, and red pepper flakes and cook until the onion is softened, about 3–4 minutes.
Add the diced tomatoes to the skillet and cook about 5 minutes to warm and combine flavors; season with additional salt to taste if needed.
When the tomato mixture is cooking, add the angel hair pasta to the boiling water and cook according to package directions, usually 4–5 minutes, until al dente; reserve some pasta cooking water and drain.
Lower the skillet heat to low, stir in the heavy cream and grated Parmesan, and bring to a gentle simmer until the cheese melts and the sauce thickens slightly.
Return the cooked chicken to the skillet and stir to combine with the sauce; adjust seasoning as needed.
Add the drained pasta and chopped parsley to the skillet, tossing gently to coat. If the sauce is too thick, add a splash of reserved hot pasta water to loosen it.
Serve immediately.