The source of all that might be right (or wrong) has this to say:
The issue of whether it is acceptable to use the term "Union Jack" is one that causes considerable controversy. Although it is often asserted that "Union Jack" should only be used for the flag when it is flown as a jack (a small flag flown at the bow of a ship), it is not universally accepted that the "Jack" of "Union Jack" is a reference to such a jack flag; other explanations have been put forward (see ). The term possibly dates from the early 1700s, but its origin is uncertain. The word Jack may have come from the name of the James VI, King of Scots who inherited the English crown, causing the flag to be designed, that is Jac from Jacobus, Latin for James. Even if the term "Union Jack" does derive from the jack flag (as perhaps seems most likely), after three centuries, it is now sanctioned by usage, has appeared in official usage, and remains the popular term. The BBC website disregards the term "union flag" because of its "great potential for confusion", preferring union jack (in lower case) (see ). The term "Union Flag", on the other hand, is the term preferred in official documents by vexillologists. The Merchant Shipping Act 1995 (c. 21) section 4(1)(a)(ii) refers to the national colours of the United Kingdom as "the Union flag (commonly known as the Union Jack)".
Because Wales is not a kingdom in its own right. It is a Principality which had been conquered by England. Scotland and Ireland were voluntarily absorbed into the 'United Kingdom' by the first and second Acts Of Union.