Taste and season with more salt and olive oil as desired. Assemble salad: Put farro in a large bowl. Drizzle on vinegar and season with a big pinch of salt and chile flakes. Toss thoroughly.
Once the broth has come to a simmer, return chicken to skillet, skin-side up. Carefully transfer to the oven and roast until farro is tender and chicken skin is crisp, 30 minutes.