Whisk buttermilk, flour, mustard, salt, five-spice powder, onion powder, and granulated garlic in large bowl until smooth. Add chicken and toss to coat. Cover and refrigerate for at least 4 hours or up to 24 hours.

Adjust oven rack to middle position and heat oven to 350 degrees. Spread Tianjin chiles and Sichuan peppercorns on rimmed baking sheet and toast in oven until fragrant, about 4 minutes. Set aside and let cool completely.

Combine cooled Tianjin chiles and Sichuan peppercorns in blender jar. Process on medium speed until coarsely ground, about 30 seconds. Increase speed to high and continue to process to fine powder, about 1 minute longer. Without removing blender lid, let sit until chile dust settles, about 5 minutes; transfer chile mixture to bowl.

Whisk vinegar powder, sugar, salt, and monosodium glutamate into chile mixture until combined. Melt duck fat in medium saucepan over medium heat. Off heat, whisk oil and chile mixture into duck fat; set aside.

Whisk all ingredients in large bowl until combined.

Set wire rack in rimmed baking sheet. Add oil to large Dutch oven until it measures 1½ inches deep. Heat oil over medium-high heat to 325 degrees. Working with half of chicken, dredge in flour mixture, pressing to adhere. Lightly shake off excess flour mixture and add chicken to hot oil. Fry, turning occasionally, until chicken registers 155 degrees, 8 to 10 minutes, adjusting heat as needed to maintain oil temperature between 300 and 325 degrees. Transfer chicken to prepared rack. Return oil to 325 degrees and repeat dredging and frying with remaining chicken and flour mixture.

Return oil to 325 degrees and return first batch of chicken to oil. Fry until dark meat registers 175 degrees and white meat registers 160 degrees, 2 to 5 minutes. Return chicken to rack. Return oil to 325 degrees and repeat frying with remaining chicken.

Whisk chile oil to recombine, then gently warm over medium-low heat, about 2 minutes; remove from heat. Working with 1 piece at a time, dunk chicken pieces in chile oil, turning to coat completely, then transfer to platter. Serve.