Step 1: Preheat the grill to screaming hot
Step 2: Place the sugar in a shallow bowl and stir in the cinnamon with a fork. Arrange the pineapple slices on a large plate. Brush the tops with coconut milk. Invert the slices and brush with coconut milk again.
Step 3: Soon the ice cream into bowl and keep cold in the freezer.
Step 4: Brush and oil the grill grate. Dip each pineapple slice in the cinnamon sugar on both sides (use tongs or a fork), shaking off the excess. Arrange the pineapple slices on the grill grate. Grill until caramelized (dark brown) on both side, about 5 minutes per side. (Give each slice a quarter turn half way through to lay on a crosshatch of grill marks.)
Step 5: Transfer the grilled pineapple to the bowls with the ice cream.
Step 6: Heat the rum in a small saucepan until warm, almost hot, but do not let boil. Touch a match to the rum and pour it over the pineapple. Serve at once.