Stir together the garlic powder, onion powder, kosher salt, ground black pepper, and smoked paprika in a small bowl. Set aside.
Pour the chicken broth, apple cider vinegar, and liquid smoke into the Instant Pot inner pot.
Add the chicken breasts to the pot.
Sprinkle the seasoning blend over the chicken.
Close and lock the lid. Press manual high pressure and adjust the cooking time to 10 minutes. It should take about 10 minutes to come to pressure (more if your liquids were cold).
When the cooking time has finished, let the pressure release naturally for 15 minutes.
Turn the pressure release valve to venting to release any remaining pressure and unlock the lid.
Drain off all but 1 cup of the cooking liquid.
Shred the chicken, and stir in the desired amount of barbecue sauce.
For more flavor, let the chicken sit in the saucy liquid for about 10 minutes before serving.
Notes
Seasoning blend: Feel free to substitute your favorite bbq seasoning blend for the seasonings.
Vinegar: You can decrease the amount of vinegar if you prefer. The vinegar helps to make the chicken tender, so I don't recommend omitting it.