Yep. The Welsh Dragon. It's officially called Y Ddraig Goch, but since that just means "The Red Dragon" I wouldn't worry about it too much.
...It Hasn't Been On The Welsh Flag For Very Long
The dragon was only made the official Welsh flag in 1959. Before that, there was this flag, known as the flag of St David, which is a lot more boring.
...But Red Dragons Have Represented Wales For Much Longer.
The Historia Brittonum (History of the Britons) dates back to about 800 BC and describes England and Wales as white and red serpents struggling under the ground. This later turned into an Arthurian legend, which went something like this...
A long time ago in Britain, there was a king called Lludd and a red dragon. The red dragon was constantly fighting a white dragon, that invaded from another town. The red dragon would shriek in pain, and it was such a horrid noise that it caused plants, animals, and even unborn babies to die. Lludd, after asking advice from his wiser brother, dug a deep pit in the middle of Britain and filled it with mead. Both dragons dived into it, drank the mead and fell asleep, allowing Lludd to capture them and imprison them at Dinas Emrys in North Wales.
And this is the good bit with Merlin in it....
Hundreds of years later, King Vortigern wanted to build a castle at Dinas Emrys. But every night, whatever he built was "demolished by unseen forces". His advisors tell him that if he finds a boy with no natural father, and sacrifices him on the site of the castle, then the castle would then stand. The king finds such a boy, who turns out to be Merlin. Merlin tells him about the two dragons and the king releases them. This time the red dragon kills the white dragon, and it's all good,
Merlin tells Vortigern that the white dragon is symbolic of the invading Saxons, and that the red dragon is symbolic of Vortigern's people, who would later become the Welsh.
There's more about Owain Glyndwr and how his banner was the Golden Dragon, which he used when he fought the English in battle, but I'm going to save him for another time. Suffice to say, that eventually, the dragon ended up on the Welsh flag!