Heat the oil in a large pot over medium heat. Add the celery, onion, and carrot and saute, stirring occasionally, until the veggies are mostly tender, about 8 minutes.
Stir in the garlic and cook for 30-60 seconds. Stir in the flour, Italian seasoning, red pepper flakes, and salt and pepper. Cook for a couple of minutes, then stir and cook for another couple of minutes to make a roux.
Slowly stir in the broth and bring to a simmer. Let simmer for 5 minutes, then add the cooked chicken, spinach, and milk. Return to a simmer.
Add the gnocchi and cook until the gnocchi float to the top and are cooked through, about 2-5 minutes.
Serve hot with lemon wedges to drizzle plus grated parmesan if desired!