Place 2 cups of the sugar in a heavy saucepan and cook over medium heat, stirring regularly, until caramelized.
Pour the caramel into a 9-inch-round, 3-inch-deep pan (or divide among 12 individual ramekins), turning to coat the bottom and sides. Set aside for 15 minutes.
In a large bowl, mix the milks, eggs, coconut extract, vanilla extract, and salt.
Pour the mixture over the caramel. Set in a water bath and cover with foil.
Bake until the center is set, 2 1/2 to 3 hours. Chill for 3 hours or overnight.
Before serving, turn the flan onto a serving plate.
Heat the remaining sugar in 1 cup water over medium-high heat until it dissolves, about 30 seconds. Stir in the coconut and spoon over the flan.