To make the caramel, bring 1 cup of sugar and ½ cup of water to a boil over medium heat and boil until it gets a deep amber color, about 8-10 minutes.
Pour the hot caramel into the previously buttered flan molds or ramekins and try to distribute it evenly on the bottom of the molds.
Combine the pineapple juice with the sugar and tapioca starch in a small saucepan over low heat and bring to a boil, keep an eye on it as it is prone to boil over, let simmer until it begins to thicken, about 5-8 minutes, remove and cool completely.
Pre-heat oven to 350 F
Beat the eggs on low speed; slowly mix in the pineapple mixture, the milk, the vanilla, and the rum until well combined
Strain the flan mixture and pour into the caramel coated molds.
Place the flan molds in the oven dish with water – the water should cover at least ½ of the height of the ramekins - and bake until the flans solidify, about 45-50 minutes.
Let the flans cool completely, then refrigerate for a couple of hour.
To help release the flans place the ramekins in a bowl with warm water before serving to melt the caramel and loosen the flan.
Serve alone or accompanied by fresh berries or with caramelized pineapple slices