Prep the chicken: Pat the chicken dry.
In a shallow bowl, mix flour, salt, pepper, and paprika. Lightly coat the chicken in the seasoned flour, shaking off excess.
Boil the pasta (if using): Cook according to package directions in salted water. Reserve 1/2 cup pasta water, then drain.
Brown the chicken: Heat 2 tablespoons olive oil and 1 tablespoon butter in a large skillet over medium-high heat.
Sear chicken in batches, 2–3 minutes per side, until golden and just cooked through. Transfer to a plate and tent loosely with foil.
Sauté the aromatics: Lower heat to medium. Add remaining 1 tablespoon olive oil and 1 tablespoon butter.
Stir in garlic and red pepper flakes. Cook 30–60 seconds until fragrant, not browned.
Deglaze and simmer: Pour in white wine, scraping up any browned bits. Let it bubble for 1–2 minutes.
Add chicken broth and simmer another 2 minutes to reduce slightly.
Finish the sauce: Stir in lemon zest, lemon juice, and capers. Whisk in remaining 2 tablespoons butter until the sauce looks glossy. Taste and adjust salt, pepper, and lemon.
Combine: Return chicken and any juices to the pan.
Toss gently to coat. If serving with pasta, add cooked pasta and a splash of reserved pasta water to help the sauce cling.
Garnish and serve: Sprinkle with parsley and Parmesan if you like. Serve immediately with extra lemon wedges.