Combine the apple cider, cranberries, ginger, red chile flakes, star anise, cloves, allspice, orange slices and 2 of the cinnamon sticks in a medium pot. Bring to a simmer and cook for 5 minutes. Turn off the heat and allow the cider to sit for 5 minutes. Strain the cider to remove the spices.
If desired, put 1 ounce dark rum in each of 4 large mugs. Divide the cider among the mugs and garnish with the remaining cinnamon sticks.