Combine hoisin sauce, barbecue sauce, soy sauce and red pepper flakes in Instant Pot; mix well. Add chicken; stir to coat.
Secure lid and move pressure release valve to Sealing position. Press Pressure Cook or Manual; cook at High Pressure 8 Minutes.
When cooking is complete, use natural release for 5 Minutes, then release remaining pressure. Remove chicken to large plate; let stand until cool enough to handle. Shred chicken into bite-size pieces.
Stir water into cornstarch in small bowl until smooth. Press Sauté; add cornstarch mixture to pot. Cook and stir about 2 Minutes or until sauce thickens. Return chicken to pot; mix well. Spoon about ¼ cup chicken mixture onto each roll; serve with onion and pickles, if desired.