Preheat the oven to 350F.
In a medium saucepan over medium-low heat, melt sugar for caramel until liquefied and it has dissolved into a golden-light brown syrup.
Carefully pour hot syrup into a nine-inch round glass baking dish or flan pot, turning the dish side to side to evenly coat the bottom and sides. Set aside.
In a large bowl, with an electric mixer or blender, mix eggs, condensed milk, evaporated milk, vanilla extract, rum and sugar until smooth. Add the dissolved corn starch. Pour the mixture into the caramel-coated pan.
Place the baking dish or flan pot in a larger baking dish; add enough hot water to the lager pan to come halfway up the side of the baking dish or flan pot.
Bake for 45 minutes to 1 hour or until a knife inserted near the center comes out clean. Cool slightly. Carefully remove flan from water, place it on a wire rack and allow it to cool completely. Refrigerate for several hours or overnight. Wait to unmold onto a plate before serving.
To serve, place a plate on top of the flan, grab a hold of both the plate and the pan, and quickly and carefully flip it over so that the flan is now upside down. Carefully lift of the flan or dishpan. Before inverting make sure it is not stuck around the edges. Run a small knife around the edges if needed.
Decorate with peaches, cherries or strawberries.