In a large mixing bowl, combine the shredded chicken, mozzarella cheese, cream cheese, mayonnaise, minced garlic, garlic powder, onion powder, salt, and black pepper. Mix until well combined and creamy.
Lay out the flour tortillas on a clean surface. Spread an equal amount of the chicken mixture onto each tortilla, leaving about an inch border around the edges.
Top the chicken mixture with fresh spinach leaves, diced tomatoes, and parsley if using.
Roll each tortilla tightly, folding in the sides as you go to secure the filling.
Heat a skillet over medium heat and add a drizzle of olive oil. Place the wraps seam-side down in the skillet and cook for 3-4 minutes on each side, or until golden brown and crispy.
Remove from the skillet and let cool for a minute before slicing in half. Serve warm.