In a small bowl, whisk together oil, lime zest, lime juice, vinegar, honey, garlic, and red pepper flakes.
In a large bowl, combine chicken, squash, onion, and mushrooms. Pour oil mixture over, tossing gently to coat. Cover and refrigerate for 30 minutes.
Remove chicken and vegetables, discarding marinade. Thread chicken and vegetables alternately onto 12-inch water-soaked skewers.
Grill chicken kabobs, covered with grill lid, over medium-high heat (350 to 400) for 15 to 20 minutes, or until done, turning occasionally.
Serve with hot cooked rice and Lime Butter Sauce.