Season chicken with salt and pepper. In a large nonstick skillet, heat 1 tablespoon oil over high heat. Add half the chicken; cook, stirring constantly, until opaque throughout, 2 to 4 minutes. Transfer to a plate. Repeat with remaining chicken.
Add remaining tablespoon oil to pan, along with the onion and bell pepper. Cook, stirring constantly, until onion is tender and golden, about 4 minutes (reduce heat if browning too quickly).
Reduce heat to medium; add garlic, ginger, and red-pepper flakes; cook, stirring, until fragrant, 30 to 60 seconds.
Stir in soy sauce, vinegar, and cornstarch mixture; remove from heat. Add chicken and any accumulated juices; toss to coat. Serve in lettuce cups.