Let the chicken wings sit at room temperature for 30 minutes. In a large, deep skillet with a lid, heat the oil until the temperature registers 300 degrees on a deep-fry thermometer, about 5 minutes.
Preheat the oven to 300 degrees and line a rimmed baking sheet with paper towels. Season the wings with the salt, then toss in the flour to coat. Add half of the wings to the oil, partially cover the pan and fry, turning occasionally with tongs, until golden-brown, 12 to 15 minutes. Transfer to the prepared baking sheet; blot with the paper towels, then discard the towels. Keep the first batch of wings warm in the oven while you repeat the process with the remaining wings.
In a bowl, combine the butter and hot sauce. Add the wings; toss to coat. Serve with celery sticks and blue cheese dressing for dipping.