Heat grill or grill pan to medium-high heat.
Put potatoes in a large saucepan and add enough water to cover by 2 inches. Bring to a boil and cook until just tender, about 10 minutes. Add corn, cook for 1 minute, and drain well.
Meanwhile, season chicken with salt and pepper. Grill, turning once, until cooked through, about 15 minutes. Transfer to a cutting board and let rest.
While chicken grills, heat oil in a large skillet over medium heat. Add panko and cook, stirring often, until toasted and golden brown, 3 to 4 minutes. Transfer to a plate to cool completely.
Add ketchup, LEA & PERRINS® Worcestershire sauce, soy sauce, sugar, and mustard to the same skillet, set over low heat, and stir until bubbling and smooth. Transfer all but 2 Tbsp. to a bowl. Add vinegar to skillet and stir well, then add potatoes and corn and stir until evenly coated. Divide among serving plates.
Spread reserved sauce all over chicken, then cut into strips. Divide among serving plates, then sprinkle chicken with reserved panko. Garnish with scallions and serve immediately.