Place the chicken thighs, sliced andouille, onion, green bell pepper, celery, garlic, Cajun seasoning, chicken broth, and fire-roasted tomatoes into the slow cooker. Stir once to combine.
Cover and cook on low for 6 hours until the chicken is very tender.
Remove the chicken, shred it with two forks, and return it to the pot. Stir the mixture well.
In a mixing bowl, stir together the flour, baking powder, and salt. Add the milk and melted butter and mix just until a soft dough forms.
Drop spoonfuls of the dough over the surface of the stew. Cover and cook on high for 1 hour until the dumplings are cooked through.
Ladle into bowls and top each serving with chopped green onions.