Combine 1/3 cup of flour, paprika, salt, and black pepper in a food storage bag. Put chicken in bag and toss to coat.
Whisk together the egg and water. Dip the coated chicken in the egg and water mixture. Combine the corn flakes with the ½ cup of flour; roll the chicken in the corn flake mixture.
Heat the butter in a skillet over medium heat; add the chicken and brown it well on all sides. Lower the heat, and continue to cook, by turning occasionally, for 35 to 40 minutes, or until the chicken is tender and juices run clear.