Heat oil in a large heavy skillet over medium-high heat, or deep-fryer to 375 degrees F (190 degrees C).

Place flour in a shallow baking pan and stir in 1 teaspoon of salt and 1 teaspoon of pepper. In a medium bowl, whisk together egg whites, milk, vinegar, and remaining salt and pepper until frothy.

Dip onion rings in wet ingredients then into flour mixture until coated. Then dip in egg white mixture again, and then into flour again.

Fry onion rings in hot oil a few at a time so they are not crowded, until golden brown. Drain on paper towels, and serve immediately.