Put the flour in a pie plate; season with salt and pepper. Dredge the fish in the flour, tapping off the excess; transfer to a plate.
In a large skillet, melt 1 tablespoon of the butter in 1 tablespoon of the oil. Add half of the fillets and cook over high heat, turning once, until golden and crisp, 3 to 4 minutes. Transfer to a platter, cover with foil and keep warm. Repeat with another 1 tablespoon each of butter and oil and the remaining fish.
Add the remaining 1 1/2 tablespoons of butter and the almonds to the skillet. Cook over high heat, stirring, until golden, 2 minutes. Add the capers and lemon slices and cook until heated through, 1 minute longer. Spoon the sauce over the fish and serve.