1. Prepare the marinade by whisking together Greek yogurt, olive oil, garlic, paprika, cumin, cinnamon, crushed red pepper flakes, oregano, lemon zest, lemon juice, vinegar, salt, and pepper until smooth.
2. Trim excess fat from the chicken and cut into uniform bite-sized pieces for even cooking.
3. Place the chicken in the marinade, ensuring all pieces are coated thoroughly. Cover and refrigerate for at least eight hours or overnight for thighs, or 30 minutes to 4 hours if using breasts to avoid mushiness from the acid.
4. If using wooden skewers, soak them in water for 20 to 30 minutes before assembling.
5. Thread the chicken pieces onto skewers, alternating with vegetables like onions, bell peppers, and zucchini if desired, spacing evenly but not overcrowding. Metal skewers are preferred as they are sturdy and reusable.
6. Preheat the grill to medium-high heat, and grease the grates well with oil to prevent sticking.
7. Grill the kabobs approximately 13 to 15 minutes for thighs (about 10 minutes for breasts), turning every few minutes to cook evenly and baste with leftover marinade if desired, until golden brown and cooked through.
8. Use a metal spatula to help release any pieces that stick to the grill.
9. Transfer kabobs to a platter, garnish with crumbled feta cheese and parsley if desired, and serve immediately with accompaniments such as tzatziki sauce, pita bread, or a Greek salad.