Choppr ins an extension for Opera and that adds a short flic.kr-url to the right hand column on a Flickr™ photo page.
This short url is calculated from the photo's unique id (actually, the calculation is ”bijective“, thus could be inverted) – there is no web service contacted during that process.
You find the short url behind a little ☆-icon below the photo's license statement and above its privacy information in the right hand info column.
Install the extension (there are Presto and Chromium/Blink variants, the latter more up to date) from Opera's Addons page by simply clicking on the ”Install“ button there:
An additional download url providing development versions and access to an online repository may be provided later.