Combine chicken and soy sauce in a glass or ceramic bowl and let marinate in the refrigerator for 1 hour.
Remove chicken from the marinade and shake off excess. Discard the remaining marinade.
Heat oil in a large wok to 350 degrees F (175 degrees C).
While the oil is heating, whisk flour, 2 tablespoons cornstarch, and black pepper together in a shallow dish. Dredge chicken in flour mixture.
Fry chicken in batches in the hot oil until golden brown and crispy and no longer pink in the centers, 5 to 8 minutes per batch. Remove to a plate.
Discard any oil remaining in the wok. Return the wok to medium-high heat and add sugar, 1/2 cup water, and vinegar. Heat through, stirring frequently until sugar dissolves. Add onion and continue cooking for 1 minute.
Meanwhile, mix remaining cornstarch into remaining 1/2 cup water and stir until completely mixed. Add to vinegar mixture in the pan along with pineapples and bell pepper chunks. Continue cooking until sauce thickens and bell peppers are just cooked, about 3 minutes. Add chicken and toss to coat.