Put the skate fillets in a dish large enough to hold them in one layer. Pour the milk over them and sprinkle with salt and pepper to taste. Turn the fillets in the milk so they are coated on both sides.
Scatter the flour over a large dish. Lightly dredge the fillets in the flour on both sides.
Heat the oil in a large nonstick skillet over medium-high heat. When the oil is hot but not smoking, add the fillets. If it is necessary to do this in two batches, use the same oil. Saute on one side until golden brown, about 3 minutes. Turn and cook on the other side until golden brown, about 3 minutes more. When the fillets are done, transfer them to a warm platter or serving plate.
Wipe out the pan with a paper towel and return the skillet to the heat. Melt the butter and add the red peppers, shaking the pan frequently until the butter turns light brown. Add the capers, cook briefly, and add the shallots, vinegar and parsley. Cook briefly; then stir and pour the sauce over each fillet evenly. Serve immediately.