Yahoo has released a feature that lets people.
The Twitter2Flickr feature requires that you enable Flickr as an approved application that can tweet under your username.
Then, when you click the "blog this" link above a photo at Flickr, you're presented with the option to twitter it. The tweet will come with a "flic.kr" shortened URL.
Flickr has a large number of users, and its use is amplified by the fact that other sites can make use of Flickr data through an API (application programming interface). The Twitter integration is a modest example of Yahoo's attempt to make its sites less of a walled garden by working better with other Web properties.
A Twitter search for Flickr photographs indicates that a lot of people are making use of the integration, which had been in beta testing since earlier in June.