Pat the shrimp dry and season with the salt and pepper. Heat the oil in a large, nonstick skillet or sauté pan over medium-high heat. Sear the shrimp in the hot oil until they are bright pink and curling, about 2 minutes. Stir in the grapes, lemon zest, lime zest, jalapeño, and ginger. Pour on the rum and carefully ignite, keeping your hands and face away from any flame. Simmer 1 minute. Stir in the brown sugar, lemon juice, and lime juice and simmer until the sauce is slightly syrupy and the shrimp are just cooked through, 2 to 3 minutes.

Arrange shrimp on a serving platter or on individual dishes, spoon on the grape sauce and serve.