Whisk the buttermilk, hot sauce, 1/4 teaspoon salt and a few grinds of pepper in a medium bowl. Transfer 3 tablespoons of the buttermilk mixture to a small bowl and whisk in the mayonnaise; set aside. Add the chicken thighs to the bowl with the remaining buttermilk mixture; toss to coat and set aside.
Bake the waffle fries as the label directs. Meanwhile, combine the cake flour, 1/2 teaspoon salt and 1/4 teaspoon pepper in a shallow dish. Heat 1/2 inch vegetable oil in a large Dutch oven or pot over medium-high heat. Dredge the chicken in the flour mixture and shake off the excess. Fry until golden and cooked through, 4 to 5 minutes per side. Transfer to a rack set over a baking sheet to drain.
Season the waffle fries with pepper. Divide the buttermilk mayonnaise among the roll bottoms. Top with lettuce, the chicken, pickles and the roll tops; serve with the waffle fries.
If you don?t have any cake flour on hand, you can combine 3?4 cup plus 2 tablespoons all-purpose flour with 2 tablespoons cornstarch, then sift a few times.