Pound chicken breasts to an even 1/2-inch thickness, then cut each crosswise in half to create 4 sandwich-sized pieces.
Whisk together buttermilk, hot sauce, paprika, garlic powder, onion powder, salt, pepper, and cayenne. Add chicken, coat thoroughly, cover, and refrigerate for at least 1 hour, up to 24 hours.
Combine mayonnaise, hot sauce, paprika, garlic powder, cayenne, onion powder, and pickle juice if using. Whisk until smooth. Cover and refrigerate until assembly.
Whisk together flour, cornstarch, baking powder, paprika, garlic powder, onion powder, salt, pepper, and cayenne. Drizzle 3-4 tablespoons of the buttermilk marinade into the flour and stir with a fork until small clumps form.
Remove chicken from marinade, letting excess drip off. Press firmly into the flour mixture, dip briefly back into the marinade, then press again into the flour. Place breaded chicken on a wire rack and rest for 10-15 minutes.
Heat oil in a large deep pot to 350°F (175°C). Fry chicken in batches of 2 for 4-5 minutes per side, until golden brown and internal temperature reaches 165°F (74°C). Drain on a wire rack.
Melt butter in a skillet over medium heat. Toast the brioche buns cut-side down for 1-2 minutes until golden and crisp.
Spread spicy mayo on both cut surfaces of each bun. Layer pickle chips on the bottom bun, place the fried chicken on top, and close with the top bun. Serve immediately.