Lightly coat a 5-quart or larger slow cooker with nonstick spray. In a small bowl, stir together the hoisin sauce, soy sauce, rice vinegar, and sesame oil. Set aside.
Heat the olive oil in a large skillet over medium high. Add the ground chicken and brown the meat, breaking it into small pieces. Continue cooking until no longer pink, about 4 to 6 minutes. Stir in the white and light green parts of the green onions, ginger, and garlic. Cook 30 additional seconds.
Transfer the meat mixture to the slow cooker. Stir in the chopped mushrooms, carrots, red pepper flakes, and sauce. Cover and cook on LOW for 2 to 3 hours until the mixture is thickened and the chicken is ultra tender.
Stir in the water chestnuts and green parts of the green onions before serving. To serve, separate the butter lettuce leaves and fill with the chicken mixture. Enjoy hot.