Add ground chicken, salt, oregano, and red pepper flakes and cooking, stirring frequently and using a spatula to break up the meat, until chicken is cooked through and any liquid has evaporated. Stir in the tomatoes, gnocchi, and tomato paste and raise heat to medium-high. Cook until meat sauce is thickened and no longer watery, 4 to 5 minutes. Stir in parmesan. Smooth out the gnocchi and meat sauce. Tear up the mozzarella with your hands and place it on top of the gnocchi and meat sauce.