Flick.to.twitt is a simple service where you upload a photo through their web interface (no registration required) and it posts an announcement to Twitter at the same time.
You do have to allow this site to post on Flickr through their normal authorization step, but otherwise the site does a good job of not storing any of your personal information (even the Flickr stuff is passed off).
Now if there could be a mobile client too for phones, that would make it even more useful. But, after reading the About page this was a donated free project that someone had done personally. So we appreciate all the hard work and simple interface.