Beat egg whites in a glass or metal bowl until stiff peaks form. Lift your beater or whisk straight up: the egg whites will form sharp peaks.
Mix corn, egg yolks, flour, salt, and red pepper together in a large bowl; fold whipped egg whites into the corn mixture.
Heat oil in a large skillet over medium-high heat. Working in batches, drop corn mixture into hot oil by the tablespoonful in several spots without crowding the pan; cook until browned and set, 2 to 3 minutes per side. Repeat with remaining batter.