Preheat oven to 375 degrees F. Lightly grease a 2 12-cup muffin tins with cooking spray.
In a large bowl, combine cream cheese, mozzarella, Parmesan, artichokes, spinach, chicken, garlic, salt, pepper and red pepper flakes. Stir until well combined. Set aside.
Lay out each sheet of puff pastry on a clean, flat work surface. Cut each sheet into 9 equal squares.
Place each square of puff pastry in a greased muffin tin.
Distribute the filling evenly into each of the puff pastry cups.
Bake for 30-35 minutes, until the dough is golden and the filling cooked through.