Or rather to see the Union Flag as pedants insist it should really be called
This is because Union Jack is technically a maritime flag used to distinguish British ships. Though purists object it is popularly used to describe the the flag of the United Kingdom.
The flag is composed of symbols of the constituent parts of the UK - the red cross at the centre is the cross of St George representing England, the blue for Scotland etc.
UK? So why Team GB?
Interestingly the Olympics brings to the surface the confusion created by the terms Great Britain and the United Kingdom. Great Britain should only really refer to the core island of Britain, not the outlying islands or Northern Ireland. It would, therefore, be more logical to have a team UK.
Uncertainty is also evident in the use of flags, anthems and other national emblems. Football supporters, for example, associate God Save the Queen with the England team, despite it being the national anthem for the entire kingdom. It was striking that some of the Welsh players did not sing it with gusto before a recent GB v Brazil fixture.
This is not to imply any shortfall of loyalty to the UK in Wales. Rather it shows that rallying to the Union flag does require a suspension of normal friendly(ish) rivalries between the countries it represents.