Begin preparing the marinade. Combine all ingredients in a large mixing bowl. Cut the chicken thighs into bite-size or small pieces, then add to the yogurt mixture. Fold together to combine and evenly coat the chicken, then store in the refrigerator for a minimum of three hours (or overnight).
When ready to cook, soak the wooden kebab skewers in water for up to 30 minutes to minimize charing or burning. Meanwhile, prepare the sauce by combining all ingredients in a blender or food processor. Pulse to combine, then blend until smooth. Set aside until ready to serve.
To make the kebabs, cut the peppers and red onion into 1” pieces (large enough to thread onto kebab skewers). Slice the zucchini crosswise in ¼” to ½” coin. Remove the chicken from the fridge and fill the skewers, alternating veggies with chicken. Add any leftover veggies to a veggie-only skewer to avoid food waste.
Preheat the grill to medium heat. Clean the grates as needed and brush lighting with oil to avoid sticking. Grill the kebabs for 3-4 minutes on each side, rotating in quarter turns until fully cooked. Use a meat thermometer to verify doneness.
Transfer from the grill to a serving platter, adding the dipping sauce on the side or drizzling over the kebabs. Garnish with fresh cilantro, red pepper flakes, or fresh lime juice. Serve immediately.