In a medium saucepan over medium heat, whisk together the pineapple juice, vinegar, sugar, ketchup, soy sauce, and red pepper flakes. Bring to a boil, then reduce the heat to medium and cook uncovered for 8 minutes.
In a small bowl, stir the cornstarch with 1½ tablespoons cold water, then whisk the mixture into the sauce. Cook for 1 more minute, until the sauce thickens and becomes glossy. Remove from heat and set aside.
In a large bowl, whisk together the flour, cornstarch, baking powder, baking soda, salt, and black pepper. Add the water and 1½ tablespoons vegetable oil, whisking until a smooth batter forms. Add the chicken pieces and toss until evenly coated.
Line a plate with a few layers of paper towels. Heat 1 inch of vegetable oil in a deep-sided medium skillet or wok over medium-high heat until shimmering (about 350°F/175°C). Working in batches, use two forks to carefully lower the battered chicken, one piece at a time, into the hot oil, spacing the pieces apart to prevent sticking. Fry for about 2 minutes per side, turning once, until golden brown and crispy. Transfer the chicken to the paper towel-lined plate to drain excess oil.
In a clean large skillet or wok, heat 1 tablespoon vegetable oil over medium-high heat. Add the bell peppers and onion, stir-frying for 3 to 4 minutes until slightly tender but still crisp.
Reheat the sauce over medium heat until hot. Put the cooked chicken in the pan with the vegetables. Off the heat, gradually pour the sweet and sour sauce over everything and toss to coat. Serve immediately.
