Make the sauce. In a bowl, whisk together the BBQ sauce, broth, brown sugar, apple cider vinegar, Worcestershire, onion powder, garlic powder, smoked paprika, red pepper flakes (if using), and a pinch of salt and pepper.
Add everything to the cooker. Place the chicken in your slow cooker, Instant Pot, or a baking dish.
Pour the sauce over the top, turning the chicken to coat.
Cook it low and slow (or fast if needed). Slow cooker: 3–4 hours on High or 6–7 hours on Low, until the chicken shreds easily.
Instant Pot: Cook on High Pressure for 10–12 minutes (thighs need 10, thick breasts need 12). Natural release 5 minutes, then quick release.
Oven: Cover the baking dish tightly and bake at 325°F (165°C) for 60–75 minutes, until fork tender.
Shred the chicken. Transfer the chicken to a cutting board and shred with two forks. Return it to the sauce and toss until everything is well coated.
Adjust the sauce. Taste and add a splash more vinegar for tang, a pinch of brown sugar for sweetness, or extra BBQ sauce if you like it saucier.
If it’s too thin, let it simmer uncovered for a few minutes (use sauté mode or bake uncovered briefly).
Serve. Pile onto toasted buns with pickles and coleslaw, spoon over rice, or tuck into tortillas. Add extra sauce if you like it messy.