Preheat the oven to 325 degrees.
In a pot, combine 1 cup of the sugar, 1/4 cup of water, and a pinch of salt, and cook over low heat until the sugar melts. Continue to cook until the sugar has caramelized to a rich golden brown. Carefully pour the caramel into 1-quart flan dish, turning the dish to coat the bottom and sides with an even layer. Set aside to let the caramel cool and harden.
Combine the milk, cream, coconut milk and cinnamon stick in a saucepan and set over low heat. Bring to a simmer and continue to simmer gently for 30 minutes. Use tongs or a slotted spoon to remove and discard the cinnamon stick, then set the pan aside and let the mixture cool for 15 minutes.
Break the eggs into a bowl, beat them with a whisk, add the remaining 1/2 cup of sugar and gradually beat the hot milk mixture into the eggs in a thin, slow stream, a little at a time to avoid cooking the eggs. Pour the coconut mixture through a fine-mesh strainer into a large, heatproof measuring cup to facilitate pouring it into the custard cups.
Put the flan dish into a baking pan. Put the baking pan on the middle rack of the oven and fill the flan dish with the coconut mixture. Pour warm water into the baking pan to create a water bath coming halfway up the sides of the flan dish.
Bake until the flan is completely set and a toothpick inserted to the center of a flan comes out clean, approximately 40 to 45 minutes. Remove from the oven, carefully remove the flan dish from the water bath, and let cool completely. Cover the flan with plastic wrap, and refrigerate for at least 6 hours, or overnight. Keep refrigerated until ready to serve.
To serve, run a sharp knife around the outside of the flan dish to loosen. Invert the dish onto a plate and pop out the flan. The caramel should pour off the top and down the sides of the custard.