Mix coconut and condensed milk (2 tablespoons in a glass will be needed later) in a bowl. Add 1 teaspoon of rum (flavoring), and stir in powdered sugar until a firm mixture is formed.
Portion coconut mixture into 3 parts. Color 1 part with cocoa. Color 1 part with red food coloring. 1 part natural. Roll these into rolls about 30 cm long and about 5 cm thick.
Stick these rolls together using remaining condensed milk (2 tablespoons). Refrigerate for a few hours (preferably overnight). Cover with chocolate icing. Cut into pieces to serve.