Fill a saucepan with cold water and place over medium heat. Stir in vinegar and bring to a gentle, slow simmer. Working with one egg at a time, crack an egg into a ramekin or measuring cup for easier transfer.
Stir the water vigorously to create a whirlpool effect. As the whirlpool is turning, drop the egg into the center of the water. Continue to stir gently, cooking until the egg white turns opaque. Using a slotted spoon, carefully remove the egg from the water and move to a paper towel-lined plate to drain.
In a medium saucepan, heat oil to 375 degrees.
Meanwhile, set up a dredging station with 3 separate bowls. To the first bowl, add the flour. Beat 2 eggs with salt and pepper in a second bowl. Add breadcrumbs to the third bowl. Carefully dip the cooled egg first into the flour, second into the egg mixture, and last into the breadcrumbs, coating egg on all sides at each station.
Using a slotted spoon, carefully drop the egg into the hot oil and fry until golden brown, 2 to 3 minutes, being careful not to overcook. Drain on a paper-towel lined plate.
Garnish with pickled red onions, green onions, and red pepper flakes. Serve immediately.