Place shrimp in a large bowl. In a medium bowl, whisk together 2 tablespoons olive oil, sweet chili sauce, soy sauce, rum, garlic, lime juice, and red pepper flakes. Add 3/4 of the marinade to the bowl of shrimp and let marinate in refrigerator for 15 to 30 minutes.
Heat remaining 1 tablespoon oil in a large pan or grill pan over medium-high heat. Add shrimp and cook on one side until golden, about 2 minutes. Using tongs, flip shrimp, then brush with remaining marinade. Cook 1 to 2 minutes more.
Garnish with green onions and serve immediately.