Pour the Kahlúa into 2 warmed martini glasses. Gently float half a measure of Sambuca over the back of a spoon into each glass so that it creates a layer on top.
Pour the Bailey's and blue Curaçao into shot glasses. Next, pour the remaining Sambuca into a warmed wine glass and carefully set it alight. Carefully pour it into the martini glasses.
Pour the Bailey's and Curaçao into the lighted martini glasses at the same time. Serve with straws.