Preheat oven to 350 degrees Fahrenheit. Butter and flour (or coat with Pam Baking Spray) a 12- to 15-cup bundt pan and set aside.
In a medium bowl, combine the flour and salt. Stir with a fork until well-blended, then set aside.
In the bowl of a stand mixer, combine the butter and coconut oil. Beat until light and fluffy, 3-5 minutes.
Gradually add the sugar while continuing to beat at medium speed.
Add the eggs one at a time, beating in between until well blended.
Add the vanilla bean scrapings and rum, mixing thoroughly.
On medium-low speed, add the flour mixture in 4 additions, alternating with 1 cup of the coconut milk in 3 additions, starting and ending with the flour.
Remove bowl from mixer and fold in the flaked coconut.
Scoop into the bundt pan and spread evenly.
Bake for 1 hour 10 minutes or until the top is golden and a cake tester inserted in the middle comes out with a few crumbs attached.
Cool in bundt pan for 10 minutes (longer if using silicone; I waited 45 minutes), then cover with a large plate and invert, transferring the cake to the plate. If using a conventional pan, you may need to loosen the edges with a butter knife first.
Gradually add the remaining coconut milk to confectioners sugar, whisking, until you've reached desired consistency. This may mean more or less of the coconut milk and/or confectioners sugar.
Drizzle glaze over the slightly warm cake.
Recipe by poet in the pantry at http://poetinthepantry.com/2012/11/15/coconut-rum-bundt-cake-for-national-bundt-cake-day/