Stir together ketchup, brown sugar, red wine vinegar, soy sauce, Pickapeppa sauce, Jamaican jerk seasoning, and salt in the Instant Pot.
Add chicken pieces and stir to coat.
Close Instant Pot Lid, and make sure steam release handle is in the ‘Sealing’ position.
Cook on ‘Manual’ (or 'Pressure Cook') for 10 minutes.
Do a quick release of pressure and carefully open the Instant Pot.
Remove chicken pieces and set aside.
Press ‘Saute’ and reduce the sauce until thickened, about 5 to 7 minutes. Use a splatter screen if necessary, to prevent splatters.
Grill chicken for just enough time to get sear marks, and to give it a grilled look and flavor, about 2 minutes per side. You can either baste each side while you grill, or coat the chicken in the sauce before placing on the grill.
Serve with peach salsa or fried plantains, and beans and rice. Serve remaining sauce on the side.