Place flour for dredging in a shallow bowl. Coat each fillet with seasoned flour and shake off excess. Heat a large nonstick skillet over medium heat for 3 to 4 minutes. Add butter/olive oil combination. Add the fillets, without crowding. Increase heat to high and saute, shaking the pan from time to time, until the bottom of the fish is nicely browned, about 3 minutes. Turn and brown the other side. Remove fish to a plate and keep warm in the oven. Repeat with remaining fillets.
Deglaze the pan with white wine. Cook, stirring over high heat until reduced by about one-third. Stir in remaining butter and drained capers.