Prepare the Caramel: In a small saucepan, combine sugar and water. Cook over medium heat until the sugar dissolves and turns amber. Pour into a 9-inch baking dish and tilt to coat the bottom. Set aside to cool.
Make the Custard: Preheat oven to 350°F (175°C). In a blender, combine eggs, coconut milk, sweetened condensed milk, and vanilla extract. Blend until smooth.
Bake the Flan: Pour the custard over the caramel in the baking dish. Place the dish in a larger roasting pan and fill with hot water halfway up the sides. Bake for 50-60 minutes, or until set but slightly jiggly in the center.
Cool and Serve: Let the flan cool to room temperature, then refrigerate for at least 4 hours. To serve, run a knife around the edges and invert onto a serving plate.