It's an interesting question and one which has puzzled many since they realised that the Union Flag is supposed to be an amalgamation - or 'union' - of all the constituent countries within the Union Flag. However, the question does have an answer!
The Union Flag traces its roots to 1606 when it was originally called the Flag of Great Britain. King James VI of Scotland had inherited the thrones of England and Ireland in 1603, becoming James I, and united the thrones of England, Scotland, and Ireland, in a personal union.
However, Wales had already been conquered by England in the 13th century. Originally ruled by the Romans in its early history, England and Wales were seen as a single unit. By the time the Romans left Britain, Wales became an independent state with their own system of law.
However, during the Norman invasion of Wales in the 11th Century, English law was practised in certain areas of the country. By 1283, under the leadership of Prince Edward, the biggest army ever seen in England invaded and conquered Wales, bringing it under English rule.
Therefore, a few hundred years later when England was to be joined in the union with Scotland and Ireland, Wales was already part of "England", and thus was not represented in the new union's flag.
So in 1606, King James I issued the following decree:
Whereas, some differences hath arisen between Our subjects of South and North Britaine travelling by Seas, about the bearing of their Flagges: For the avoiding of all contentions hereafter. We have, with the advice of our Council, ordered: That from henceforth all our Subjects of this Isle and Kingdome of Great Britaine, and all our members thereof, shall beare in their main-toppe the Red Crosse, commonly called St. George’s Crosse, and the White Crosse, commonly called St. Andrew’s Crosse, joyned together according to the forme made by our heralds, and sent by Us to our Admerall to be published to our Subjects: and in their fore-toppe our Subjects of South Britaine shall weare the Red Crosse onely as they were wont, and our Subjects of North Britaine in their fore-toppe the White Crosse onely as they were accustomed.
The flag that was created to celebrate the union of England (incorporating Wales) and Scotland was the Flag of Great Britain, representing St George's Cross (the patron saint of England), superimposed on the Saltire of St Andrew (patron saint of Scotland). Despite Ireland being part of this new union, it was not represented on the flag until nearly two hundred years later!
The Flag of Great Britain was flown until 1801 until the "United Kingdom of Great Britain and Ireland" came into existence. It was only then that Ireland was recognised both formally in the name of the union, as well as its flag! By adding Saint Patrick's Saltire the Flag of this new Union is the same Union Flag that we still fly today!