I don't know how much you have seen of the new London 2012 Olympic logo, which has attracted a lot of criticism. The biggest problem with the logo itself (as opposed the flashing promotional video which caused problems for some people with epilepsy) is that it doesn't really have any symbolism. It has the Olyympic rings, the word London, and the shape almost clearly spells out "2012". Apart from these bare essentials, there is... nothing.
From what I've heard, this is quite understandable, as the designers were given criteria that ruled out nearly every symbolism the logo could draw on. The 2012 logo could not look like any previous Olympic logos, ruling out anything resembling an athlete or the Olympic flame. The logo of "the UK's games" was not allowed to be too London-centric, ruling out a vast array of images. I'm not sure whether something reppsenting the whole of Britain would have been acceptable, but I don't think the Union Flag is subtle enough for that context, and no alternative springs to mind. There really isn't much left, is there?
A similar set of restrictions have appeared in the rules for the competition for a new flag and emblem of Kosovo. In this case, the brief is less restrictive, and much more reasonable anyway. Unwanted symbols in flags can easily spark all sorts of problems, and the political sensitivites in this area are more serious than worries that the Scots will resent the extra spending on a London event.
A new flag for Kosovo needs to be acceptable to both the Serbian and Albanian residents in order to avoid sparking tensions and dooming any peaceful settlement to failure. The flag must be neutral, combining symbology, or making references only to peace or the region itself.
Unfortunately, no matter how neutral the flag is, it will only succeed if there is an acceptable settlement to start with. Removing a symbol is only a skin deep change. The deliberately inclusive/neutral flags of Ireland and Cyprus have both ultimately become associated with one side of a conflict. It would be hard to find a more intrinsically neutral flag than the Cypriot map and olive branches, but in recent years plans for reuniting the island have included a requirement for a new flag.