1. With small flower-shaped canape cutter, cut out 8 flowers from orange peel; set aside.
2. In 2-quart saucepan over medium heat, heat brandy, cloves, allspice, cinnamon sticks, sugar, and remaining orange peel until very hot. Remove from heat. Carefully ignite brandy with match. Let flame for 1 to 2 minutes.
3. Slowly pour coffee into flaming mixture. Ladle into 8 demitasse or cafe brulot cups. Garnish with orange-peel flowers.