Combine 2 tablespoons flour, salt and pepper in a shallow dish. Dredge chicken in the flour mixture. Heat 2 teaspoons oil in a large nonstick skillet over medium heat. Add the chicken and cook until golden and cooked through, 3 to 4 minutes per side, adjusting heat as necessary to prevent burning. Transfer to a plate and cover with foil to keep warm.
Increase the heat to medium-high and add the remaining 1 teaspoon oil to the pan. Add onion and sauté for 1 minute. Add apples and cook, stirring occasionally, until softened and browned, 1 to 5 minutes. Sprinkle the apples with the remaining 1 tablespoon flour and cook, stirring, for 30 seconds. Pour in stock and wine and bring to a boil, stirring constantly. Reduce heat to a steady simmer and cook, stirring occasionally, until slightly thickened, about 5 minutes. Reduce heat to low and stir in parsley. Return the chicken to the pan, turn to coat with the sauce, and cook until heated through, 3 to 5 minutes.