Question #423 (Which country inside the United Kingdom does NOT appear on its flag, the Union Jack?) claims that Isle of Wight appears on the Union Jack. I suppose that this answer was supposed to say England, otherwise both Wales and Isle of Wight would be correct answers.
The currently used Union Jack (or Union Flag if you will) is composed of the elements of the flag of England, the flag of Scotland and St Patrick’s saltire symbolizing (Northern) Ireland. Therefore, the UK country that is not represented on the Union Jack is Wales.