In a blender, combine 2 cups frozen pineapple, pineapple juice, coconut milk, coconut cream, and rum (if using.) Pulse until well blended.
Pour half the liquid into an airtight, freezer-safe container. Sprinkle in half of the flaked coconut, then pour in the remaining liquid. Plop remaining pineapple chunks into the liquid, then sprinkle with the rest of the coconut.
Freeze 3-4 hours or until solid. When ready to serve, remove from freezer about 20 minutes prior to scooping - the absence of dairy makes this ice cream freezer harder, making it more difficult to scoop straight from the freezer.