Preheat oven to 450 degrees. Place peaches and onions on a large rimmed baking sheet; season with salt and pepper. Sprinkle with ginger, soy sauce, 1 tablespoon vegetable oil, sesame oil, and red-pepper flakes; toss to coat.
Rub chicken with remaining teaspoon vegetable oil; season with salt and pepper. Arrange chicken skin side up among peaches and onions.
Roast until chicken is opaque throughout and registers 160 degrees on an instant-read thermometer inserted in thickest part of breast (avoiding bone), 25 to 30 minutes. Serve chicken with white rice, peaches, and onions.