In 1-gallon resealable food-storage plastic bag, mix vinegar, oil, basil, oregano and garlic. Add kabobs; seal bag and turn to coat. Refrigerate at least 6 hours or overnight to marinate, turning bag once or twice.
When ready to cook kabobs, heat gas or charcoal grill. When grill is heated, remove kabobs from marinade; discard marinade. Place kabobs on gas grill over medium heat or on charcoal grill over medium coals; cover grill. Cook 12 to 15 minutes, turning once, until chicken is no longer pink in center.
Spread 1 tablespoon dressing on each flat bread. Slide chicken and vegetables from kabobs off skewers and onto breads (if needed, cut chicken and vegetables into smaller pieces). Secure with toothpick, if needed.