Gently heat the first six ingredients in a chafing dish or, if one is not available, a saucepan. Pour the hot coffee into coffeemugs. The brandy should begin to release its aroma after a few minutes. At this point, ignite the brandy and allow the flames to burn for 15-20 sec, then ladle the brandy mixture over the hot coffee.
Top with whipped cream and pour a spoonful of kahlua over the whipped cream. Garnish with the cinnamon stick.