Layer the celery, carrot, onion, and garlic in the bottom of a slow cooker.
In a dish, combine the flour, salt, and pepper. Dredge the chicken on all sides in the flour mixture, then place on top of the veggies in the slow cooker. Pour in the stock and sprinkle with the thyme leaves.
Cover the slow cooker and cook on HIGH for 3 hours or LOW for 6-8 hours depending on your schedule. When the cooking time is over, the chicken should shred very easily. Remove the chicken from the slow cooker and add the gnocchi. Stir the gnocchi into the vegetable mixture and cover; cook on high for 30 minutes.
While the gnocchi is cooking, remove the skin and bones from the chicken and tear into bite-sized chunks.
After 30 minutes, taste a gnocchi to be sure it is cooked through. If it is too chewy in the center, cook for 15 minutes or until cooked through.
Add the chicken back to the slow cooker and taste; add salt and pepper to your preference until the dish is very flavorful.
If at any point the soup becomes very thick, splash in more stock to thin to your liking.
Serve with extra thyme on top, if desired. Enjoy!