In a large bowl, whisk together the vinegar, olive oil, pepper flakes, garlic, salt, cheese and oregano. Set aside.
Place the whole pitas on the hot grill and cook on each side for about 1 1/2 minutes, or until nice grill marks form and the pitas are toasty. REmove and cut each pita in half, and then into 1 inch strips.
Add the tomatoes, onion, cucumber, olives, parsley and grilled pita strips to the bowl of vinaigrette and toss together well. Serve immediately.