Whisk vinegar, soy sauce, oil, parsley, basil, oregano, garlic powder, and black pepper together in a bowl. Pour 1 cup of marinade into resealable plastic bag, add chicken, and toss to coat. Seal bag and marinate in refrigerator, at least 4 hours. Store remainder 1/2 cup in glass container (for brushing onto meat and veggies when grilling).
Preheat grill to medium-low and lightly oil grate. Drain and discard marinade. Alternately thread chicken, peppers, onions, zucchini and mushrooms onto skewers. Grill kebabs on preheated grill until chicken is no longer pink in center, 4 to 6 minutes per side (total time about 15 min). Brush marinade onto veggies and chicken every time you turn kebabs.