Season the chicken with salt and pepper and dust lightly with flour. Heat the olive oil in a large, deep skillet. Add the chicken and cook over high heat, turning once, until lightly browned, about 8 minutes. Add the onion and cook over moderate heat, stirring occasionally, until softened, about 4 minutes. Add the wine and simmer until nearly evaporated, about 3 minutes. Add the stock, cover and cook over moderately low heat for 12 minutes. Using tongs, transfer the chicken to a platter.
Boil the pan juices over moderately high heat until slightly reduced, about 12 minutes. Stir in the greens gradually, adding more as they wilt. Add the scallions and 3 tablespoons each of parsley and dill. Season with salt and pepper. Return the chicken to the skillet, cover and cook over moderate heat for 10 minutes. Stir in the lemon juice. Transfer to a platter, sprinkle with the remaining parsley and dill and serve.