Bring 3 cups water and the ginger to a boil in a medium saucepan over high heat. Add the sugar, stir until dissolved and remove from the heat. Add the hibiscus flowers, and let the tea steep for 10 minutes. Strain the tea through a fine-mesh strainer, and refrigerate it until completely cooled, about 15 minutes.
Fill 6 wineglasses with ice. Add 4 ounces of the hibiscus tea and 2 ounces of the rum to each glass. Stir, and garnish with orange wedges.
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