Combine potato and onions; squeeze moisture from potato mixture over a sieve. Combine potato mixture, flour, salt, and egg whites in a large bowl. Divide mixture into 12 equal portions, and squeeze out any remaining liquid. Discard liquid. Shape each portion into a 1/4-inch-thick patty.
Heat 1 tablespoon oil in a large nonstick skillet over medium heat. Add 6 patties to pan; cook 5 minutes on each side or until golden. Repeat procedure with remaining 1 tablespoon oil and 6 patties.