Cook sweet potato in boiling water 10 minutes or until tender, and drain. Mash sweet potato with a fork until smooth.
Place 1/2 cup sugar in a small, heavy saucepan. Cook sugar over medium heat 5 minutes or until golden, stirring as needed to dissolve the sugar evenly. Immediately pour into an 8-inch round cake pan coated with cooking spray, tipping the pan back and forth quickly until caramelized sugar coats the bottom.
Place sweet potato, 1/2 cup sugar, rum, and remaining ingredients in a large bowl, stirring well with a whisk. Pour sweet potato mixture into prepared pan. Place pan in a 13 x 9-inch baking dish; add hot water to dish to a depth of 1 inch. Bake at 300° for 1 1/2 hours or until a knife inserted in center comes out clean. Remove pan from dish; cool completely on a wire rack. Cover and chill at least 3 hours.
Loosen flan's edge with a knife or rubber spatula. Place a dessert plate, upside down, on top of the pan; invert flan onto the plate. Drizzle any remaining caramelized syrup over the flan.