Preheat oven to 400°F (200°C) and grease a 9x13-inch baking dish with cooking spray or olive oil.
In a mixing bowl, combine softened cream cheese, Parmesan, mozzarella, minced garlic, red pepper flakes, and 1/2 teaspoon salt. Stir in chopped spinach until fully combined.
In a small bowl, mix paprika, garlic powder, onion powder, black pepper, and remaining 1/2 teaspoon salt.
Pat chicken breasts dry with paper towels, drizzle with olive oil, and rub the seasoning blend evenly over all surfaces.
Using a sharp knife, cut a deep pocket into the thickest side of each breast, going about 3/4 of the way through without cutting all the way to the opposite edge.
Divide the spinach filling into four portions and stuff each pocket gently, packing it toward the back. Secure with toothpicks if desired.
Place stuffed chicken in the prepared baking dish and bake uncovered for 25-30 minutes, until internal temperature reaches 165°F (74°C).
Let chicken rest for 5 minutes, remove toothpicks if used, then serve whole or sliced on the diagonal.