Smoke duck over Southern hardwood. Once smoked, remove meat and reserve for gumbo, reserving bones for stock (you can also save the skin for cracklins). Smoking may be done up to 1 day in advance.
Cover duck bones with water in a stockpot and simmer for 2 hours. Strain stock and return to pot. Bring stock to a boil; add roux. Whisk until roux dissolves, about 15 minutes, and let simmer. Add onion, celery, bell pepper, garlic, seasoned salt, white pepper, and hot sauce. Let simmer 1 hour, until vegetables are almost wilted.
Meanwhile, cut reserved duck meat and andouille into cubes. Set aside.
Adjust seasoning of stock-roux mixture if needed, then add duck meat, andouille, green onion, and parsley. Simmer for 15 minutes. Serve hot over rice.