Preheat oven to 400°F (200°C). In a large bowl, combine chicken pieces, zucchinis, cherry tomatoes, red onion, and garlic. Drizzle with olive oil and toss to coat evenly. In a small bowl, mix dried oregano, basil, smoked paprika, salt, black pepper, and red pepper flakes. Sprinkle the seasoning mix over the chicken and vegetables, then toss again to evenly distribute. Transfer the mixture to a baking dish, spreading it out in an even layer. Bake in the preheated oven for 20 minutes. Remove from oven, sprinkle shredded mozzarella and Parmesan cheese evenly on top. Return to the oven and bake for an additional 8-10 minutes, until cheese is melted and bubbly. Garnish with fresh parsley before serving. Serve warm and enjoy a healthy Mediterranean-inspired meal.