Fill a large pot with enough oil to reach a depth of 2 inches and heat over medium-high heat until it registers 350° on a deep-fat thermometer. Working in batches, toss the pickles in the flour mixture, pressing to adhere. Shake off any excess flour, then toss gently in the eggs to coat. Coat with the flour mixture again. Shake off any excess flour, then add to the oil. Fry, turning occasionally after the pickles rise to the top, until browned, 8 to 9 minutes. Using a slotted spoon, transfer to paper towels to drain. Serve immediately.