Place the potatoes and onion into a bowl, and stir in eggs, salt, and flour as needed to make the mixture hold together. With wet hands, scoop up about 1/3 cup of the mixture per patty, and form into flat round or oval shapes.
Heat the vegetable oil in a large skillet over medium heat until it shimmers, and gently place the patties into the hot oil. Fry until the bottoms are golden brown and crisp, 5 to 8 minutes, then flip with a spatula and fry the other side until golden.
Line a colander or strainer with 2 paper towels, and drain the cooked latkes in the colander. Serve hot.