New South Wales

The flag of the Australian state of New South Wales is like most Australian state flags a blue ensign with a British Union Fag in the Canton, and a regional insignia in the fly.

Despite the name "New South Wales" there isn't any Welsh symbolism on it at all! The emblem in the fly is a cross of St George of England bearing a lion and Southern Cross.
I corrected this by changing the emblem just a little bit:

I replaced the St George's Cross with that of St David the patron saint of Wales, and the lion with the famous red dragon. The idea is really the same as the original flag but with Welsh symbols rather than English.
However if New South Wales wants to move away from British ensigns to something more original, i though of this flag:

 Its an inverted Cross of St David defaced with the Southern Cross (in the same pattern as the Australian flag). The reason I inverted the colours of the Cross of St David are:

• So it would be distinctive from the unofficial second flag of Wales
• I wanted to show a connection to Wales, but at the same time I wanted it to be Australian rather than Welsh. The same way the Nova Scotia flag symbolises a connection to Scotland but stands out as something Canadian rather than Scottish. 

I think inverting the colours was the best way to do this, Another version could have the red dragon in the canton:

However I think this might empathise the Welsh connection too much, which might defeat the point of inverting the colours in the first place. On the other hand though dragons are cool.