Arrange chicken wings on a grill pan. Cook in the Panasonic Countertop Induction Oven on "Auto Cook" setting 1 until browned, about 18 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).
Make barbeque sauce by whisking ketchup, vinegar, brown sugar, paprika, salt, pepper, and red pepper flakes together in a small sauce pan until well combined. Simmer for 5 minutes, stirring occasionally.
Place cooked wings in a large bowl; pour desired amount of sauce over top and toss to coat well.