Place the flour in a bowl, and set aside. Beat the eggs in another bowl. Mix together the crushed pretzels, Parmesan cheese, Italian seasoning, cayenne pepper, and paprika in a third bowl.
Rinse the chicken breast halves, and pat them dry with paper towels. Gently press the chicken breasts into the flour to coat, and shake off the excess flour. Dip into the beaten egg, then press into the pretzel crumb mixture. Gently toss between your hands so any crumbs that haven't stuck can fall away. Place the breaded chicken breasts onto a plate while breading the rest; do not stack.
Heat the oil in a skillet over medium heat, and fry the coated chicken breasts about 5 to 7 minutes per side, until the coating is golden brown and the juices run clear.