In a large bowl, toss the chicken with avocado oil, salt, pepper, garlic powder, paprika, cumin, and BBQ sauce. Let marinate for at least 30 minutes.
Thread the chicken onto skewers.
Preheat grill to medium-high heat. Grill skewers for 8–10 minutes, turning occasionally and brushing with extra BBQ sauce until cooked through.
In a large bowl or platter, layer romaine, arugula, tomatoes, cucumber, avocado, and red onion.
Top with grilled chicken skewers, squeeze lime juice over the salad, and garnish with cilantro.
Serve immediately with extra BBQ sauce on the side, if desired.