In a large bowl, mix buttermilk and vinegar; add chicken and toss to coat. Refrigerate, covered, 8 hours or overnight.
Remove chicken from buttermilk mixture, allowing excess to drip off chicken back into the bowl; place chicken on rimmed plate and set aside. Whisk eggs into buttermilk mixture. In a shallow dish, combine gluten-free flour, garlic powder, salt, onion powder and pepper. Dredge chicken in flour mixture, firmly patting to help coating adhere. Repeat, dipping chicken again in buttermilk mixture and then dredging in flour mixture.
Arrange on a wire rack over a baking sheet. Let stand 30 minutes.
In an Dutch oven, electric skillet or deep fryer, heat oil to 375°. Fry chicken, several pieces at a time, until chicken is golden brown and juices run clear, 6-7 minutes on each side. Drain on paper towels.