Pat chicken dry. Combine paprika, salt, pepper, and flour. Toss chicken to coat lightly, shaking off excess.
Heat olive oil and butter in a large skillet over medium-high. Sear chicken until golden, 2–3 minutes per side. Transfer to a plate.
Lower heat to medium. Sauté onion and zucchini in the same pan until lightly browned and softened, about 5 minutes.
Stir in garlic, tomato paste, smoked paprika, and red pepper flakes. Cook until fragrant, 30–45 seconds.
Pour in chicken broth and scrape up browned bits. Simmer 2 minutes to reduce slightly.
Stir in heavy cream. Return chicken and any juices. Simmer gently until thickened and chicken is cooked through, 5–7 minutes.
Finish with lemon juice and parsley. Taste and adjust salt and pepper as needed.
Rest 2 minutes off heat, then serve hot.