Preheat oven to 325F. Place 1/2-cup sugar in a medium skillet on top of stove over medium-high heat; add about 1/2 cup of water slowly and a teaspoon of vinegar, boil until water and sugar is completely dissolved, cook until the water is reduced.
Swirl the syrup around the pan. Do not let it burn, but continue cooking until sugar syrup turns medium-dark brown, about 5 minutes.
Remove from heat; pour caramelized sugar syrup into pie dish or small individual dessert dishes. Swirl syrup evenly until coats bottom of dish completely. Let it cool.
In a large bowl, add and whisk together remaining 1/4-cup sugar, salt, egg yolks, and whole eggs until combined. Add in remaining ingredients, Coco Lopez, milk, vanilla, and rum. Whisk until combined.
Pour Flan Mix into pie pan or into small individual dessert dishes. Carefully transfer pie pan or dessert dishes into the oven on the middle of baking pan, pour a cup of water so the water comes halfway up the sides of pie pan or dessert dishes, making a bain-marie. Boil water bath.
Alternatively, it can be cooked on top of a stove as long as a water bath is still used and using an aluminum foil tent seal.
Place pie pan or small individual dessert dishes in the middle of the baking pan with water bath in the oven. Bake until Flan is almost set (it will appear loose in center but will continue cooking as it cools), 45 to 50 minutes.
A good test to see if it is done: just poke a knife into the middle of the Flan and pull it out: if it comes out clean, then it's done. Carefully take out the whole baking pan out of oven or stove with the Flan dishes, until water cools; then transfer pie dish or small dessert dishes to cool. Refrigerate.
When ready to serve, run a knife between Flan and pie dish. Place a serving dish on top of Flan; invert.
Slice, and garnish with any remaining syrup or shredded coconut. Chill the Flan overnight in the pie dish or individual small dessert dishes and serve the next day.