Using a cleaver or heavy knife, cut chicken along each side of the backbone to remove it. Place chicken skin side up on a work surface. With the heal of your hand, press down on the breastbone to flatten the chicken.
In a resealable plastic bag, combine wine, olive oil, lemon juice, garlic, oregano, red-pepper flakes, and salt. Add chicken, seal the bag, and refrigerate for at least 1 hour and up to 2 hours.
Meanwhile, build a charcoal fire in one side of a grill and let it burn until the coals are covered with white ash. Place a large disposable aluminum pan on the empty side of the grill, and fill it halfway with water. If you are using a gas grill, preheat on high. Turn one burner off, and keep the other burner on high. Place the foil pan on the off burner, and fill halfway with water.
Remove the chicken from the marinade. Lightly oil the cooking grate with vegetable oil. Place chicken skin side down on the grate, over the pan of water. Weight the chicken with a heavy skillet or an aluminum foil-wrapped brick. Cover grill, and cook for 25 minutes. Remove the skillet and turn the chicken. Cover, and continue to cook until the chicken shows no sign of pink when pierced at the thighbone, about 25 minutes more.
Cut the chicken into quarters, and serve hot, accompanied by Grilled New Potatoes.