The Native American dragon was Piasa. Long snake-like tail with wings. Killed by a hero.
As for the Celts, there is a dragon legend which is central to the legend of King Arthur (who was Celtic British, remember). It goes like this:
King Vortigern, a Celtic usurper who had made the fatal mistake of inviting the Saxon tribes to Britain, was trying to build a castle, but the foundations wouldn’t stay built–the work would be undone every night. His wise men told him, “sacrifice a boy who was born without a father.” The king’s messengers rode around, heard a kid insult another kid with the no-father thing, kidnapped the insulted kid and brought him before the King.
The kid, named Merlin, once told he was to be sacrificed, decided to prove what fools the king’s advisers were. He told the King to search below the foundations. The King did, found an underground cave with an underground pool, drained the pool and found two sleeping dragons, one red, one white. The dragons woke up and started fighting. IIRC the white dragon representing the Saxons was winning at first, but then the red dragon, representing the Britons/Celts/Welsh/Cymry gained the upper hand and chased Whitey off into the night sky.
The kid Merlin prophesized: the foundations were wrecked every night because the dragons would wake up and fight. Now you can finish it, but you, King Vortigern, will be burnt inside it by Ambrosius (a rival British chieftain). At first the Saxons will win, but a king will come who will chase them away for a time.
So Vortigern gets crisped, Ambrosius takes over the anti-Saxon resistance and dies, his lieutenant Uther Pendragon takes over, Uther commits some sneaky adultery to conceive King Arthur, Arthur takes the shiv out of the stone and is revealed as rightful king, Merlin (all grown up now) helps Arthur, etc. etc.
There’s also something about Merlin moving Stonehenge from Ireland to Britain using amazing engines, and the death of Ambrosius being foretold by a star in the shape of a dragon. I don’t know if the red and white dragons ever reappear in the legend, but you know eventually Arthur died and the Anglo-Saxons (the white dragon) eventually won for good and turned Britain into England. Except Wales, Scotland and Ireland remained Celtic.
So the Celts did have dragons. And that’s why there’s a red dragon on the flag of Wales.