This is a letter that I have used in the past that seems to have a high success rate and makes clear what the person needs to do to change the flickr licensing - much easier than dealing with WP:OTRS. Obviously you need to adapt the links and specifics to the particular image.
Dear Andrew,
I am a volunteer editor of Wikipedia (wikipedia.org), the free open-content encyclopedia.
I enjoyed browsing your great photos of the World Eskimo Indian Olympics. I am writing to see if you would consider freely licensing an image of the ear pull (http://www.flickr.com/photos/ottomatona/2700875396/in/set-72157606358539386/), so that it can be used to illustrate the Wikipedia article on that subject (http://en.wikipedia.org/wiki/Ear_pull).
Wikipedia can only use your photos if you are willing to grant permission for them to be used under a free license. You can do this by using Flickr options to change the photo's licensing to Creative Commons Attribution-Share Alike - click "edit" next to "All Rights Reserved" on the photo page. (Note that Wikipedia cannot accept "No Derivatives" or "Non-Commercial" licenses.)
This means that although you retain the copyright and authorship of your own work, you are granting permission for others to use, copy, and share your materials freely, and even potentially use them commercially, so long as they do not try to claim the copyright themselves, or try to prevent others from using or copying them freely ("share-alike"). You can read this license in full at creativecommons.org/licenses/by-sa/2.0/ . Please do note that your contributions may not remain intact as submitted; this license, as well as the collaborative nature of our project, also entitles others to edit, alter, and update them at will--for example, to keep up with new information, or suit the image to a different purpose.
If you do agree to grant permission for use, we will credit you on the Wikipedia image page, state that the image is your work and is used with your permission, and provide a link back to your flickr page.
I hope you will consider accepting our request!
Jen [lastname]
[email address]
en.wikipedia.org/wiki/User:Calliopejen1
(This is based on a letter written by User:Videmus Omnia.)