This service is named “Flickr my background” and it exactly does what its named for. The tool automatically syncs your twitter background with the latest pictures in your flickr account.
And the latest image in your flickr account will be displayed as the background picture in your twitter profile. I just tested it our right now, and it worked perfectly.
Here is how you have to do it -
Step 1: Provide your email address
Step 2: Provide twitter login details.
Step 3: Validate your Flickr account.
Next you will be sent to Flickr to connect your account to Twitter. It reads -
By authorizing this link, you’ll allow the Flickr my background [A sawhorse toy] service to provide:
* Access to your photostream (including private stuff)
Click the “OK I’LL ALLOW IT” button on the next page to complete the process.
Your Twitter account’s background should now be your latest Flickr image.
And here is my photo stream with the latest pictures, and then the twitter profile with the automatically updated background image. Now, uploading another picture and will check in an hour if the image changes in twitter 
A very good tool, which you can check out at Flickr my background.
I like this tool and it makes it easy to keep your background on twitter changing and unique for people to see. Is there a way to prevent it from changing though? I just think some uploads might not work as well as backgrounds.