Don't know flickr's naming conventions, but there will certainly be links to different-sized versions - if you take a look at the link for that jpg, there's an '_m' at the end - if you change it to '_s' you get a small version. You'd expect 'l' ('L'), therefore, to give you a large one, but it doesn't - take a look at the photos on flickr yourself and see if you can work out where the big one is. Note that you'd probably need to size larger photos *down* when inserting the html (max width 400).
Failing all that, use photobucket, which definitely stores larger images.