Preheat the oven to 350 degrees F (175 degrees C).

Place 1 cup sugar in a small saucepan over medium heat. Cook gently without stirring, but shake occasionally until sugar is melted. Continue cooking until sugar turns golden brown, then pour into a large glass baking dish. Rotate and tilt the dish to spread caramel evenly over the bottom. Set aside for caramel to cool and harden, about 15 minutes.

Add condensed milk, evaporated milk, eggs, milk, coconut, and remaining 1/2 cup sugar to a blender. Blend until smooth, about 3 minutes. Pour over hardened caramel in the baking dish.

Bake in the preheated oven until custard is set, about 45 minutes. Allow flan to cool for 30 minutes at room temperature. Run a knife around the edges of the dish to separate the flan from the sides. Refrigerate until completely chilled, 8 hours to overnight.

To serve, carefully invert flan onto a rimmed serving plate; let caramel sauce flow over flan.