Pat chicken dry. In a bowl, combine 1.0 teaspoon salt, 0.5 teaspoon pepper, garlic powder, and smoked paprika; rub evenly over the chicken.
Heat olive oil in a large skillet over medium-high. Sear chicken until lightly browned, about 3 to 4 minutes per side.
Reduce heat to medium-low. Add BBQ sauce, apple cider vinegar, and brown sugar. Cover and simmer until chicken reaches 165°F and is tender, about 8 to 10 minutes. Transfer to a board and shred, then return to the sauce and toss to coat.
Meanwhile, make the slaw: In a bowl, whisk mayonnaise, lemon juice, Dijon, and the remaining 0.25 teaspoon salt and 0.25 teaspoon pepper. Add coleslaw mix and toss to coat.
Toast buns: Melt butter in a skillet over medium heat. Place buns cut-side down until golden, about 1 to 2 minutes.
Assemble: Pile saucy shredded chicken onto buns. Top with slaw, pickle chips, and red onion. Serve immediately.
Notes
For a smokier flavor, use a hickory-style BBQ sauce. Swap brioche with potato rolls or sandwich bread. The chicken and slaw keep well refrigerated for up to 3 days; toast buns just before serving.