Why is wales not represent on the flag?

Because when the Union Jack was designed, Wales was not officially recognised as having seperate nation status- officially, it was classed as being part of England, so the Red Dragon was not included.

Nowadays, most Welsh people would not WANT it to be included though- national pride has grown to the extent that the majority of Welsh see their alliegance to their own flag first, and the Union Jack second (if at all!)