First, remove all flaking material. Carefully use a brass wire brush, this should remove all of the flaking stain and clear finish. If there is still some remaining you might have to get inventive but be careful and do not sand the door, sanding will destroy the fiberglass and leave a noticeable spot or area.
Now clean the door with some mild dish soap and warm water. You can use a scrubbing sponge, this could be helpful to remove more flaking stain. Make sure to rinse the door with fresh water and allow it to dry completely.
From this point it is the same as painting any other door. Prime with an oil based primer. I recommend Zinsser Cover Stain. A small splash of mineral spirits (paint thinner) in the primer will help with brushing. You can roll on the primer with a small roller, 1/4 inch thickness, but you will need to lay off the primer with a brush. This will help get the primer into all crevices.
One coat of primer should be enough.
Painting is the same as the priming. Choose a satin or semi-gloss paint as these will clean up better and last longer.
Check-out <a href="https://www.house-painting-info.com/painting-doors.html">Painting Doors</a> for more specific information.