1. In a medium bowl, whisk together Greek yogurt, olive oil, paprika, cumin, cinnamon, crushed red pepper flakes, lemon zest, lemon juice, vinegar, salt, pepper, and minced garlic to create the marinade.
2. Trim excess fat from the chicken and cut into evenly sized pieces, about 1 to 1½ inches.
3. Thread chicken pieces and red onion chunks alternately onto metal or soaked wooden skewers, leaving space between pieces. Add optional vegetables if desired. Use approximately 6–8 skewers.
4. Place the skewers on a foil-lined baking sheet, brush generously with marinade, and cover. Refrigerate for at least 8 hours or overnight for best flavor; if using chicken breasts, marinate up to 4 hours to prevent mushiness.
5. Preheat grill to medium-high heat. Grease grates by dipping a wad of paper towels in vegetable oil and rubbing carefully with tongs to prevent sticking.
6. Grill kabobs for 13 to 15 minutes, turning occasionally until golden brown and cooked through. Use a metal spatula or tongs to gently loosen if they stick to the grill.
7. Remove kabobs and transfer to a serving platter. Garnish with crumbled feta and chopped parsley if desired, and serve with tzatziki sauce and lemon wedges for an authentic touch.