Preheat the oven to 350°F. Grease a 10-inch pie plate and set aside.
Blend the eggnog, coconut flakes, sugar, flour, eggs, butter, and rum extract in a blender until completely combined. You can also use an immersion blender with the ingredients in a bowl is needed.
Pour the mixture into the prepared pie plate, then sprinkle the nutmeg on top of the filling.
Bake in the preheated oven for 45 minutes or until the pie is set in the middle. The middle will still jiggle, but will be firm and not liquid.
Remove the pie and let it cool at room temperature until the pie plate is no longer hot. Then, transfer the pie to the refrigerator and cool it completely.