Peel the banana and cut into slices. Transfer to a resealable plastic freezer bag. Seal the bag and freeze for at least 3 hours, until the bananas are frozen solid.
In a food processor, process the frozen banana, mango, and coconut water until thick and creamy, stopping occasionally to scrape down the sides of the bowl.
For a soft-serve texture, divide the nice cream between 2 bowls and serve immediately. For a firmer texture, transfer to a shallow dish, cover with plastic wrap, and freeze until firm, about 2 hours. Before serving, sprinkle with the coconut flakes.
