Lightly whisk together the oil and vinegar in a small bowl. Stir in the chiles and let stand for 5 to 10 minutes.
Slice the fluke into very thin slices, about 1/8-inch thick, using a very sharp knife. Slice the melon into similar paper-thin pieces. Arrange the melon and fish, alternating slices, on each of 4 chilled salad plates.
Drizzle the dressing and chiles lightly over the fish and onto the plates with a spoon. Sprinkle some lemon salt over the fish and serve immediately.