Fun fact: there are only two countries in the world that have pictures of dragons on their flags. One is Wales. What is the other?
The "Union Jack" - the flag that represents the United Kingdom- consists of the Cross of St. Andrew (symbol of Scotland) imposed upon the Cross of St. George (symbol of England). The background is blue, the red "vertical shaped cross" is St. George, and the white "X shaped cross" is St. Andrew (the Confederate Battle flag was patterned after it). After 1800 they stuck a red X shaped cross into the Union Jack to represent Ireland, even though its not an Irish symbol. The equivalent saint would be Patrick, whose only symbol I am aware of is the shepherds' hook.
There IS something called an "Irish cross" which actually predated Christianity in Ireland, but its nothing like the red X on the Union Jack
But they never bothered representing Wales on the Union Jack at all! Doesnt seem fair to me. So how do you remedy that injustice?
Sticking that dragon onto the Union Jack seems both graphically, thematically, messed up. Three crosses and an animal figure? How does THAT work? But since Wales also has a history of using a gold, or yellow, cross, as a national symbol I would think that it would be pretty simple to stick that onto the Union Jack somehow...slap a yellow cross in with the three other crosses.