Add chicken, artichoke hearts, cauliflower, cream cheese, broth, onion, milk, garlic powder, salt, pepper, onion powder and crushed red pepper to a 6-quart slow cooker; stir to combine. Cover and cook until an instant-read thermometer inserted in the thickest portion of chicken registers 165°F, about 4 hours on High or 6 to 7 hours on Low. Transfer the chicken to a cutting board; shred, using 2 forks.
Whisk cream and flour together in a small bowl until smooth; stir into the soup. Stir in mozzarella, spinach and the shredded chicken. Cover and cook on High until the soup is thickened and the spinach is wilted, about 15 minutes; stir.
Divide the soup among 8 shallow bowls. Sprinkle with parsley and chives.
