Preheat the oven to 450 degrees F. Make the sweet-and-sour sauce: Whisk the ketchup, marmalade, soy sauce, vinegar, ginger and cayenne in a small bowl. Put the bell peppers and scallions on a rimmed baking sheet and toss with 2 tablespoons of the prepared sauce, 1 1/2 teaspoons olive oil and a pinch of salt.
Heat the remaining 1 1/2 teaspoons olive oil in a large skillet over medium-high heat. Sprinkle the chicken with 1/2 teaspoon salt. Working in batches, add the chicken to the skillet skin-side down and cook, undisturbed, until the skin is golden and slightly crisp, about 4 minutes. Place skin-side up on the baking sheet with the vegetables.
Brush the chicken with half of the remaining sweet-and-sour sauce. Bake until a thermometer inserted into the thickest part registers 165 degrees F, 20 to 25 minutes. Divide the chicken and vegetables among plates. Serve with rice and the remaining sauce.