Make the Caramel:

1. Prepare the Caramel: In a medium saucepan, combine the sugar and water over medium heat. Stir gently until the sugar dissolves. Once the sugar has dissolved, stop stirring and allow the mixture to come to a boil. Continue boiling until the caramel turns a golden amber color.
2. Pour the Caramel: Carefully pour the hot caramel into the bottom of an 8-inch round baking dish, swirling the dish to coat the bottom evenly. Be cautious, as the caramel will be very hot.

Prepare the Flan:

3. Preheat the Oven: Preheat your oven to 325°F (160°C).
4. Heat the Dairy Mixture: In a medium saucepan, combine the coconut milk, heavy cream, and whole milk. Heat the mixture over medium heat until it is hot but not boiling, stirring occasionally. Remove from heat and set aside.
5. Whisk the Eggs: In a separate mixing bowl, whisk together the eggs, sugar, vanilla extract, and rum (if using) until well combined and slightly frothy.
6. Combine the Mixtures: Gradually pour the warm milk mixture into the egg mixture while continuously whisking to avoid curdling the eggs. Strain the custard through a fine mesh sieve into another bowl to remove any cooked egg bits.

Bake the Flan:

7. Add the Shredded Coconut: Stir the shredded coconut into the custard mixture, then pour it over the caramel in the prepared baking dish.
8. Set Up the Water Bath: Place the baking dish into a larger roasting pan. Carefully pour hot water into the roasting pan until it reaches halfway up the sides of the flan dish. This will help cook the flan evenly.
9. Bake: Bake the flan in the preheated oven for 1 hour to 1 hour 10 minutes, or until the flan is set but still slightly wobbly in the center.
10. Cool and Chill: Remove the flan from the oven and allow it to cool to room temperature. Once cooled, cover with plastic wrap and refrigerate for at least 2-3 hours to allow the flavors to develop and the custard to set.