Pulse the cilantro, parsley, shallot, and garlic in a food processor until finely chopped.
Remove the herb mixture from the food processor. Whisk in the olive oil, red wine vinegar, lime juice, salt, red pepper flakes, and pepper.
Set a 1/3 of the sauce aside for a marinade, refrigerate the rest of the sauce for later.
For the Kebabs:
Cut the chicken breasts into 1” cubes and place the cubes in a medium-size bowl or plastic bag. Add a ⅓ of the chimichurri sauce and mix until the chicken is completely covered. Cover the bowl (or close the bag) and place in the refrigerator to marinate for 2-4 hours.
If you're using wooden skewers, soak them in water for 20-30 minutes before using.
Heat the grill on medium-high heat.
When the chicken is finished marinating, remove it from the bag or bowl and discard the excess marinade. Alternate the chicken, zucchini, squash, and onion on the skewers, then spoon 1 tablespoon of chimichurri sauce over each kebab.
Grill until the chicken is cooked through and veggies are soft, about 12 to 15 minutes, turning once during this time.
Serve warm with the remainder of the chimichurri sauce (also delicious spooned over rice or quinoa).