There is no identified scriptural source for this, which is meant to be from one of Padmasambhava’s terma texts. The earliest version of this apocrypha appears in the US in the 1980s, suggesting that it is a bit made-up. However, to be more generous, this may be a poetic mash-up of earlier sources, perhaps intended to resonate for modern times. Thus, the 9th Century Prophecy of the Khotanese Arhat (a Dunhuang document) declares “A bodhisattva will take birth as the king of the Red-Faced Ones and the practice of the true dharma will come to the land of Tibet” (I’m using Sam Van Schaik’s translation there).
Here, Red-Faced Ones in Tibetan is gdong-dmar (pron. dongmar) and refers very explicitly to Tibetans. The king in this case is Songtsen Gampo, who was (and is) regarded as a great bodhisattva, builder of the Jokhang Temple and founder of Lhasa.
More generously still, the first temple Songtsen Gampo ever founded was Trandruk in the Yarlung Valley, whose name means Thundering Falcon, referring to a magical bird summoned by Songtsen Gampo to kill a great water spirit that had flooded the valley. The bird is described as having wings of iron (hence, iron bird?) which it used to cut off the five heads of the naga spirit. This last tale is taken from a 16th C pilgrimage guide to Trandruk Temple (check out Per Sorensen’s book on the subject if you’re interested).
So, this MIGHT suggest that elements if the “myth” were recycled mash-ups from the life of Songtsen Gampo (150 years before Padmasambhava), but (again, to be generous) Tibetan prophecies have always been written with a certain vagueness to them - to echo through history in the way that trulku and terma also resonate, century after century.
This, by the way, is only a suggested interpretation of my own: I have no idea whether Sam Van Schaik or Per Sorensen would agree!