Combine vinegar, brown sugar, salt, hot sauce, and black pepper in your Instant Pot's insert, stirring or whisking to combine. Add chicken breasts.
Close Instant Pot lid (making sure the "venting" steam release knob is set to sealing, not venting). Select Manual, High Pressure, 8 minutes if using fresh or already-thawed chicken or 13 minutes if using frozen chicken breasts that are NOT thawed. (It takes my 6-quart Instant Pot Duo60 about 7-8 minutes to build enough pressure to seal and begin the 8-minute cook time, and an extra 4-6 minutes to build pressure if I'm starting with frozen chicken.)
When cook time is completed, allow Instant Pot to sit (natural release) for 10 minutes, and then manually vent to relieve any residual pressure, and open the Instant Pot.
Remove chicken from Instant Pot and shred. Stir about ¾ cup cooking liquid into chicken. Discard the additional cooking liquid, or reserve it to pass at the table for those people who like saucier BBQ. (See note about using the additional liquid if making a larger batch.)
Serve on buns with coleslaw on top or as an accompaniment on the side, and pass hot sauce if desired.
