Heat 1/4 inch of oil in a large skillet over medium-high heat.
Put the flour in a shallow bowl and add some salt and pepper. Put the egg in a second shallow bowl. Put the cereal in a resealable plastic bag and pound into crumbs with your hands until mostly broken up with some bigger pieces. Transfer the cereal to a third shallow bowl.
Dip the chicken strips first in the flour, then the egg and then the cereal. Cook the strips in batches until golden brown and cooked through, 5 to 7 minutes. Drain on paper towels.
Stir together the ketchup, applesauce and Worcestershire sauce in a small bowl. Serve as a dip with the chicken fingers.