Cut the chicken breasts into 1-inch pieces and place in a large ziplock bag, shallow baking dish, or bowl.
In a separate bowl or liquid measuring cup, whisk together the olive oil, vinegar, honey, garlic, oregano, thyme, salt, and pepper.
Pour over the chicken and stir to coat (or seal the bag, removing as much air as possible, and “squish” to coat). Place in the refrigerator to marinate for 30 minutes or up to 3 hours (do not let the chicken sit for longer or the vinegar will cause it to break down). If using wooden skewers, place the skewers in water to soak for at least 20 minutes.
When ready to grill, preheat the grill to medium-high heat (about 375 degrees F). Brush the grill grates with canola oil or coat with nonstick grill spray.
Thread the kabobs: Thread a piece of chicken onto the skewer (shake off the excess marinade when removing it from the bag. Add alternating pieces of the red onion, zucchini, yellow squash, and red bell pepper until you've reached the end of the skewer, ending with chicken. Repeat with the remaining skewers, then discard the excess chicken marinade.
Grill the chicken until fully cooked through and the juices run clear, about 10 to 15 minutes, turning the skewers every few minutes so that each side has grill marks. Transfer to a serving plate and squeeze the lemon over the top. Sprinkle with fresh herbs and feta. Serve warm.