In a container large enough to hold all and keep chicken covered, soak the chicken in the buttermilk for at least 30 minutes or overnight. The lactic acids tenderize the chicken.
Mix the flour, salt, black pepper, ground celery seed and cayenne together in a bowl. Dredge each chicken piece in the seasoned flour to coat well.
Heat about 1/2 inch of combined oils in a cast iron pan or frying pan until it reaches 350˚ on a candy thermometer. In small batches not to over crowd and steam, place a few chicken tenders in the oil at a time and fry for 6 to 8 minutes. With tongs turn each piece over, then cover the pan to cook for an additional 6 minutes. Drain on paper towels and salt well.