Still working on this one, but thought I'd post it.

Enter a Flickr User ID (found in a user's RSS feed, for example: 19784312@N00).  A random image from that user's Flickr account will display on your Google hompage and update each time the page refreshes.

Working on being able to allow users to enter their Flickr username rather than user ID.  Any suggestions are appreciated.

To get the ID from a username, you'll need to use this method from the Flickr API:
www.flickr.com/services/api/flickr.peopl...

Look at my module's source for an example:
www.googlemodules.com/module/84/