Check the fish for small bones and use tweezers to pull out any that you find. Mix the flour with the salt and pepper and spread out over a large plate. Pat the fish fillets in the flour so they are evenly coated, and shake off any excess.
Heat the oil in a large frying pan over a high heat. When the oil is smoking hot, place the fish fillets in the pan and lower the heat to medium. Cook on one side until golden brown, 1 to 2 minutes, and then turn the fillets over and cook until the second side is golden brown, for a further 1 to 2 minutes. (Flatfish fillets need only 1 to 2 minutes cooking on each side. If you're cooking thicker slices--1 inch/2 to 3 centimeters thick--or fillets from a fish like trout, then 3 to 4 minutes on each side should be fine.) Remove the fish from the pan and wrap in aluminium foil to keep warm.
Wipe the pan with paper towels and return to a medium heat. Add the cubes of butter and heat until they melt and become light brown, and then turn off the heat and add the lemon juice (stand back a little as it will splutter). Add the capers if using and the parsley, and swirl the contents of the pan around. Return the fish to the pan, spoon over the juices and serve immediately.