Preheat oven to 450°F with rack in middle. Peel parsnips and quarter lengthwise. (If large, cut lengthwise into eighths and cut out cores.) Toss with 1 tablespoon oil in a large shallow baking pan and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Roast, stirring occasionally, while preparing chicken (about 5 minutes). Pat chicken dry, then sprinkle with 1 1/2 teaspoons salt and 1/2 teaspoon pepper. Heat 1 tablespoon oil in a 12-inch heavy skillet over high heat until it shimmers, then brown skin side of chicken, about 3 minutes. Transfer chicken, skin side up, to pan with parsnips, reserving skillet, and roast until chicken is cooked through and parsnips are tender and caramelized, about 20 minutes. While chicken roasts, reheat fat in skillet with remaining tablespoon oil, then add vinegar and red-pepper flakes and boil, stirring, 30 seconds. Pour into a cup and keep warm, covered. Serve chicken and fries drizzled with spicy vinegar.