Season the chicken thighs with salt and pepper.
Heat 1 tablespoon oil in a large Dutch oven or deep skillet over medium-high heat.
Add the chicken thighs and brown for 2–3 minutes per side. The chicken does not need to be cooked through at this point.
While the chicken browns, whisk together the peach preserves, BBQ sauce, apple cider vinegar, Dijon mustard, garlic powder, onion powder, and red pepper flakes.
Reduce the heat to medium-low and pour the peach barbecue sauce over the chicken.
Cover and simmer gently for 25–35 minutes, turning the chicken once or twice, until the chicken is very tender and cooked through.
Remove the lid and shred the chicken directly in the pot using two forks.
Simmer uncovered for another 5–10 minutes, stirring occasionally, until the sauce thickens and clings to the shredded chicken.
Serve warm on sandwich buns.