Pound the chicken thighs to an even 1/2-inch thickness and soak them in the buttermilk and hot sauce for 20 minutes.
Whisk the flour with the salt, lift each thigh from the buttermilk and press it firmly into the flour mixture.
Heat the vegetable oil in a deep heavy pot to 350°F, keeping the pot no more than halfway full.
Fry 2 thighs at a time for 6 to 8 minutes, turning once and maintaining 340°F to 350°F, until crisp and the centers reach 165°F.
Drain the chicken on a wire rack and carefully measure 1/3 cup hot frying oil into a heatproof bowl.
Whisk the cayenne, brown sugar, paprika and garlic powder into the measured oil and brush the mixture over both sides of each fried thigh.
Place one hot chicken thigh and 4 pickle chips in each bun, close the sandwiches and serve immediately.