Very important tip: Make sure that you have a thermometer and the oil does not go above 350, if so the flour will fry too quick and leave you with burnt crispy chicken.
Pour oil into a large heavy pot fitted with thermometer to come halfway up sides. Heat over medium-high until thermometer registers 350°. Working in 2 batches, fry chicken, turning often and adjusting heat to maintain temperature, until deep golden brown, 5–8 minutes per batch. Transfer to a wire rack set over paper towels to drain.
Heat a dry large skillet, preferably cast iron, over medium. Brush cut sides of buns with butter and, working in batches, cook, cut side down, until deep golden brown, about 2 minutes per batch.
Mix together coleslaw mixture and half of the aioli.
With the remaining aioli, mix in 1 Tbsp. pickle brine OR hot sauce in a medium bowl. (this is used to coat the bun
Spread some of the aioli over cut sides of buns. Build sandwiches with fried chicken, hot sauce, slaw, avocado and pickles if desired.