In a 1-1/2-qt. slow cooker, combine the chicken, broth, garlic, sugar, soy sauce, oyster sauce and red pepper flakes. Cook, covered, on low 2 1/2 hours or until cooked through. Remove chicken; shred with 2 forks. Return to slow cooker. Stir in 1-1/2 cups basil and hoisin sauce; heat through.
Serve in lettuce leaves with rice, green onions, carrots, radishes and remaining basil.