Whisk together chicken broth and arrowroot flour until no lumps remain. Set aside.
Chop onion, bell pepper, celery as noted and peel and smash garlic.
Place chicken in the bottom of the slow cooker and toss in the onion, bell pepper, celery, garlic, and bay leaves. Sprinkle cajun seasoning and thyme over everything.
Pour in the diced tomatoes and chicken broth. Cook on low for 8 hours or on high for 4 hours.
When the gumbo has 30 minutes left, slice up the sausages and green onions. Add the sausage, shrimp and 3/4 of the green onions to the slow cooker. Cook for the remaining 30 minutes until the shrimp is cooked through.
Shred the chicken with two forks. Ladle gumbo into bowls, sprinkle with remaining green onions and serve.