Pat chicken dry. Season lightly with some salt and pepper.
Whisk flour with remaining salt and pepper in a shallow dish.
Dredge chicken in flour, shaking off excess.
Heat olive oil and 1 tablespoon butter in a large skillet over medium-high.
Sear chicken until golden and just cooked, 3–4 minutes per side. Transfer to a plate.
Lower heat to medium. Sauté garlic 30 seconds in the same pan.
Deglaze with white wine, scraping browned bits. Reduce by half, about 2 minutes.
Stir in broth, lemon juice, capers, lemon zest, and red pepper flakes. Simmer 3 minutes.
Whisk in remaining 2 tablespoons butter. Return chicken and simmer 2–3 minutes to thicken.
Sprinkle with parsley. Taste and adjust seasoning. Serve with extra sauce spooned over.