My first idea isn't strictly keeping with the story as I reduced the Swans to two, and attempted to get the swan necks to form a heart, which is also a common Irish symbol often seen on Celtic style broaches and jewellery. I also included the Harp on the current flag.
My next two designs are more accurate according to the myth, featuring four swans, although two are upside down. Thus giving the impression of a reflection.
I have to say I like the last two designs, and think they would make a pretty cool President's Office logo if not a flag.