Place chicken breast halves between two sheets of heavy-duty plastic wrap, and flatten to 1/4" thickness, using a meat mallet or rolling pin.
Combine flour, salt, and red pepper in a shallow dish; dredge chicken in mixture, shaking off excess.
Heat 2 tablespoons oil in a large skillet over medium-high heat until hot; add half of chicken, and brown on both sides. Remove from skillet, and set aside. Repeat procedure with remaining 2 tablespoons oil and chicken.
Place half of chicken in bottom of a 3 1/2- or 4-quart electric slow cooker; top with onion, garlic, dried apple, and dried cranberries. Top with remaining chicken. Combine chicken broth and allspice; pour over chicken.
Cover and cook on HIGH setting for 2 1/2 to 3 hours. Or cook on HIGH setting for 1 hour; reduce heat and cook on LOW 4 to 4 1/2 hours. Serve with hot cooked rice, if desired.