For the chicken: Add the chicken, BBQ sauce, honey, vinegar, salt, chipotles, garlic and onion to a multi-cooker along with 1/4 cup of water and toss to combine. Cover and position the vent to Sealing. Set to pressure cook on high and set the timer to 12 minutes.
When the time is up, quick-release the steam, then remove the lid. Remove the chicken to a large bowl and shred with 2 forks. Add the sauce to the meat in 1/4-cup increments until it has become saucy but not soupy. Reserve the remaining sauce for serving or freeze for future use (see Cook's Note).
For the potatoes: Preheat the oven to 400 degrees F.
Prick each potato all over with a fork. Rub vegetable oil on each potato and bake on a baking sheet for 1 hour. Slice the potatoes lengthwise three-quarters of the way through. Add 2 cups chicken, 1/2 cup sour cream, 1/2 cup Cheddar, 1/4 cup green onion and drizzle of reserved sauce to each potato. Serve immediately.
To reheat frozen sauce, simply thaw, then tip into a skillet and reheat until warm, 5 to 7 minutes.