In a bowl, add pineapple and top with coconut rum. Let sit for 5-10 minutes.
Meanwhile, blend coconut cream and sugar until well combined. Add pineapple with coconut rum and coconut flakes to blender. Pulse just a tad as you want pieces of rum-infused pineapple in the popsicles.
Add the mixture to a popsicle mold and add popsicle sticks. Freeze for about 4 hours or up to overnight. Serve immediately after thawing mold at room temperature.