Combine the condensed milk, evaporated milk, coconut milk, sweetened cream of coconut, cream cheese, eggs, spices, vanilla extract, and rum in a blender. An immersion blender works very well here too. Blend until completely smooth. Using a fine mesh strainer, strain custard mixture over a large measuring cup with a lip and set aside. Prepare the rum caramel.
Make the rum caramel -
Combine the sugar, watter, dark rum, and cinnamon stick in a medium saucepan. Stir until the sugar is completely coated by the liquids and somewhat dissolved.
Cook over medium/high head and bring to a boil, without stirring, until the caramel turns a copper brown color. This can take anywhere from 8-15 minutes depending on your stove, so please make sure watch it so it doesn't burn.
Using a very heavy dish towel or oven mitts. grab the saucepan handle and quickly (but carefully) pour the caramel over the bottom of each ramekin. Please be careful as caramel is extremely hot.
Immediately following the caramel, pour the custard into the ramekins. Do not fill ramekins to the top. Place the roasting pans or cookie sheets in the oven and pour water about halfway up the side of your flan vessel. Bake for about 60 minutes or until knife inserted in the center comes out mostly clean. When nudged the flan should jiggle slightly.