Because Apple won't allow it. One likely reason: It would allow you to run a separate app that is not approved (or purchased) through the iTunes store. Apple cites other reasons too, of course, like battery drainage, memory consumption, etc.
Just google "iphone flash" and you'll fine tons of stories about this.
I think the question is why AA made the widget using flash, knowing it wouldn't work on the iPhone, rather than why Apple won't allow flash.