Combine chicken broth, chicken thighs, diced tomatoes, onion, carrots, water, celery, garlic, basil leaves, salt, pepper, and red pepper flakes in a slow cooker. Stir well and cover.
Cook on Low until chicken is tender and flavors combine, about 7 hours.
Stir to break up chicken. Add frozen vegetables and rice.
Cover and cook on High until rice is tender, about 1 hour.