In a medium saucepan, add sugar and melt it over medium heat, stirring occasionally until it reaches a golden amber color, about 8-10 minutes. Once melted, pour the caramel into the bottom of an ungreased loaf pan to coat evenly. Let it cool.

In a large mixing bowl, whisk together the sweetened condensed milk, coconut milk, large eggs, vanilla extract, and unsweetened shredded coconut until smooth and combine. Pour the flan mixture over the hardened caramel in the loaf pan.

Place the loaf pan in a larger baking dish or roasting pan. Pour hot water into the larger dish until it reaches about 1/4 up the sides of the loaf pan. Preheat your oven to 350°F (180°C).

Bake the flan for 50-55 minutes, or until the top is golden and feels firm to the touch. Let it cool at room temperature for about 30 minutes before refrigerating for at least three hours.

To serve, fill a shallow dish with warm water and place the flan pan into it for 10 minutes. Run a knife around the edges, then invert the pan onto a serving plate.