Preheat the oven to 350 degrees F. Bring a full kettle to the boil for a water bath.
Melt 1 cup sugar with a spoonful of water in a heavy-bottomed saucepan over medium-high heat until the sugar dissolves. Do not stir with a spoon. Swirl the pan slightly over the heat, until the sugar turns golden. Pour the sugar into an 8-inch metal cake pan, swirl to coat the bottom and sides. The sugar will harden in about 5 minutes.
Meanwhile, whisk together the coconut milk, eggs, rum and remaining 1/2 cup sugar. Strain the custard over the hardened caramel. Scatter over the lime zest and toasted coconut, and swirl a bit with a spoon to blend evenly. Set the cake pan in a roasting pan and add enough boiling water to come halfway up the cake pan. Bake in the water bath until set, about 40 minutes. Cool. Refrigerate the flan at least 4 hours before serving. When ready, dip the bottom of the pan in warm water, place a large plate over the top of the pan, and invert. The flan should unmold easily with the caramel sauce.
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