Thanks for the query.
Jan 1, 1801.
The "Union Jack" or The "Union Flag" or the British Flag is a composite design made up of three different National symbols.
1. St. George's Cross, The Flag of England
2. St. Andrew's Cross, The Flag of Scotland
3. St. Patrick's Cross, The Flag of Ireland
The first composite design for The Flag of Great Britain was done on 12th April, 1606 when the Red Cross of England was superimposed on the White Cross of Scotland. The flag attained its present design on Jan 1, 1801, with the unification of Ireland with Great Britain.
Source: http://www.know-britain.com/general/union_jack.html