In a shallow bowl combine flour, 1 1/2 tsp of the salt, and pepper and stir to combine. Dredge fish in flour, shaking to remove any excess.
Heat oil in skillet over medium-high heat until very hot but not smoking. Add 1 Tbsp butter and cook fish until golden brown, 1 to 2 minutes per side. Transfer to a plate and set aside. Deglaze the pan with wine and bring to a boil, scraping to remove any browned bits from bottom of pan. When wine has reduced by half, add chicken broth, garlic, lemon juice, and capers, and cook for 5 minutes or until slightly thickened. Whisk in remaining 1/2 tsp salt, butter, and parsley. When butter has melted, return fish to pan and cook until heated through and sauce has thickened, about 1 minute. Serve over linguine or rice.