Preheat your barbecue to medium-high. Place the oil in a large cast iron or other barbecue-safe skillet and set directly on the heat.
When the oil is hot, add the garlic, anchovies and chili flakes, and cook until fragrant, about 1 minute. Mix in the strained tomatoes or tomato sauce, wine, olives and capers and simmer the sauce 5 minutes. Set the fish in the sauce, close the lid of the barbecue, and cook 10 to 12 minutes, or until the fish is cooked through. Plate the fish, top with sauce, sprinkle with basil and serve.