Grease a 9x13" baking sheet and line with plastic wrap to at least cover the bottom. You can skip the plastic wrap if your baking sheet is pristine (mine is not).
Add coconut milk to a microwave-safe bowl and microwave for 1 to 1 1/2 minutes until hot. Add gelatin slowly, whisking the coconut milk while adding the gelatin. Allow to cool for a few minutes before adding rum. If you notice that the gelatin has clumped up a bit, pour the coconut milk mixture through a strainer into the lined baking sheet. Allow to set up in the refrigerator for at least 1 hour or until firm to the touch.
Repeat process with orange and yellow layers, microwaving the juice and water instead of coconut milk.
Allow all 3 layers to set up for at least 1 hour (or overnight) before slicing into bite size pieces. I cut mine into 9 x 6 rows for 54 pieces.