Grill flounder whole over medium heat directly on the grill grates. Let the flounder cook uncovered for five minutes before lifting it slightly to keep it from sticking to the grill grates and falling apart. Let the flounder sit for another two to three minutes before turning it over. Continue cooking the fish for up to 10 minutes or until the meat viewed inside the cuts looks clear and opaque.
Before grilling, begin by making sure that flounder is gutted and scaled. Prepare the fish by making three diagonal cuts into each side of its body. Rub the entirety of the fish with one tablespoon of vegetable oil, and salt and pepper to taste, making sure to work the oil and seasoning into the cuts. Heat the grill grates with high heat until they are hot, and turn down the heat to medium. If using a coal fed grill, spread the coals out evenly so as to provide a uniform layer of heat once the fish is placed on the grill. Clean the grill grates with a wire brush, and place the fish on the grill. Once the flounder is done, remove it from the grill, squeeze on some lemon juice and serve it whole.
When grilling a flounder fillet, follow the same procedure. However, since flounder is generally a flaky fish when cooked, it is best to not cook the fillet directly on the grill grates. Instead, use a piece of aluminum foil or a grill boat to house the fish while it is being cooked.