Pat the chicken breasts dry and place them on a cutting board.
Using a sharp knife, cut a pocket into the side of each chicken breast without cutting through to the other side.
Brush both sides of the chicken breasts with the olive oil.
In a small bowl, combine paprika, 1/2 teaspoon salt, garlic powder, dried basil, and onion powder; mix well.
Sprinkle the spice mixture evenly over both sides of the chicken and rub it in with your hands.
In a medium bowl, stir together the softened cream cheese, mozzarella, Parmesan, chopped spinach, minced garlic, red pepper flakes, and the remaining 1/2 teaspoon salt until evenly combined.
Divide the cheese and spinach mixture among the chicken breasts and stuff it into each pocket.
Place the stuffed chicken breasts in a single layer in the air fryer basket (work in batches if needed).
Air fry at 375°F for 15–20 minutes, or until the chicken is browned and a thermometer inserted into the thickest part reads 165°F.
Keep cooked chicken covered with foil while you cook any remaining batches.