Place chicken breasts and thighs in 2-gallon resealable plastic bag.
Pour oil mixture over; seal bag. Turn bag to coat chicken with marinade. Chill overnight.
Preheat oven to 475°F.
Transfer chicken to rimmed baking sheet, shaking off marinade.
Sprinkle chicken all over with flour.
Heat 1 tablespoon peanut oil in large skillet over medium-high heat. Working in batches, add chicken to skillet. Cook until golden, adding more oil as needed, about 3 minutes per side. Return chicken to baking sheet, skin side up. Roast until cooked through, about 15 minutes.