Preheat oven to 350 degrees F (175 degrees C). Grease 6 (4-ounce) ramekins.

Slowly melt sugar in a large skillet over low heat, stirring constantly, until browned but not scorched, about 8 minutes. Divide caramel equally among the ramekins and allow to cool.

Combine whole milk, coconut milk, evaporated milk, sweetened condensed milk, and vanilla extract in a saucepan over low heat. Stir continuously until it begins to steam, about 5 minutes.

Whisk 3 eggs together in a bowl; slowly pour beaten eggs into the warm milk mixture, whisking constantly until the custard is combined.

Place ramekins in a casserole dish and fill with boiling water to reach halfway up the sides of the ramekins. Divide custard evenly among ramekins, over the caramel sauce, about 1/2 inch from the top. Cover casserole dish tightly with foil. Bake in the preheated oven until the custard is set, about 1 hour. A knife gently inserted into the center of a flan should come out clean.

Remove ramekins from the water bath and allow to cool to room temperature. Refrigerate for 2 to 3 hours before serving to chill completely. Run the tip of a paring knife around the edges to release the flan. Place a plate over the top of the ramekin and flip to release the flan onto the plate, caramel side up.