Preheat grill or grill pan to medium-high heat. If using wooden skewers, soak them in water for 20–30 minutes to prevent burning.
In a bowl, toss the zucchini, eggplant, and cherry tomatoes with olive oil, salt, and pepper. Thread the vegetables onto skewers, alternating for variety.
In a separate bowl, whisk together all chimichurri ingredients: parsley, cilantro, garlic, red wine vinegar, red pepper flakes (if using), olive oil, salt, and pepper. Set half the sauce aside for serving.
Grill the skewers for 8–10 minutes, turning occasionally, until vegetables are tender and lightly charred. During the last few minutes of cooking, brush the skewers with chimichurri sauce.
Remove from heat and drizzle with reserved chimichurri before serving.