It's a 0.8% chance that any card will be legendary, so each pack has 5 chances, but also that's a 0.8% chance that the card will be any legendary, not necessarily the Diamond Dragon. The Diamond Dragon will be 1 of 12 possible legendary cards currently available in the Untamed set, so the math works out to about a 0.333% chance of each pack getting a Diamond Dragon.
There are around 200k packs eligible (between packs purchased through the site and the crowdfund) so there should be around 650 Diamond Dragons airdropped in total and ~13 gold foil versions, although that number can vary significantly.
Then going forward Diamond Dragons will be able to be obtained by opening packs just like all of the other cards in the set.