Cook oil and flour in a large Dutch oven over medium-low heat, whisking constantly, until roux is chocolate colored (about 35 to 40 minutes).
Stir in celery, onion, and bell pepper; cook 7 minutes, stirring often. Add garlic; cook 2 minutes. Gradually stir in Duck Stock and next 8 ingredients; bring to a boil. Reduce heat, and simmer, uncovered, 1 hour, stirring occasionally.
Add duck meat; simmer 15 minutes. Remove from heat; stir in oysters and fresh basil. Let stand 5 minutes. Serve over hot rice. Sprinkle with green onions.