Combine rice, coconut milk, milk, sugar, vanilla bean, and salt, in a heavy-bottomed saucepan and bring to a boil. Reduce the heat and cover the pot, leaving the lid slightly ajar. Simmer for 30 minutes. Stir the pot occasionally with a wooden spoon until the mixture has a creamy consistency.
Soak the gelatin sheets in cold water until they soften, about 6 minutes. Take the coconut mixture off the heat, squeeze the excess water from the sheets of gelatin, and add to the coconut mixture. Stir to dissolve the gelatin. Remove the vanilla bean, and divide the pudding into 4 (3-ounce) ramekins.
Chill overnight. To unmold the puddings, place ramekins into a hot water bath for about 30 seconds and invert on a plate. Garnish with mango slices.