1. Light a fire in your grill.
2. In a small bowl, combine the olive oil, garlic, red pepper flakes, and salt and pepper and mix well. Dry the skirt steak with paper towels, then rub it generously with this mixture, pressing gently to be sure it adheres.
3. When the fire has died down and the coals are covered with white ash, check the temperature: you want a hot fire here (you can hold your hand 5 inches above the grill surface for 1 to 2 seconds). Place the steak on the grill and sear well on one side, about 4 minutes. Turn and continue cooking to the desired doneness, about 6 minutes more for rare. To check for doneness, nick, peek, and cheat: Make a ¼-inch cut in the thickest part of the meat and take a peek; it should be slightly less done than you like it. Remove the meat from the grill, cover it loosely with foil, and let it rest while you prepare the dressing.
4. In a large bowl, whisk together the olive oil, lemon juice, oregano, and salt and pepper until well combined. Add the lettuce, olives, cucumber, and tomato and toss well to thoroughly coat with the dressing, then crumble the feta cheese on top.
5. Slice the steak very thin on the bias against the grain. Place the salad on a serving platter or individual plates, top with the slices of steak, and serve.