At this very moment in v1.5 it's not possible to use the Download Button for Flickr galleries. It would be nice if that would actually be possible. A lot of users of our website would like to download photos of our annual event on their smartphones as well, but that's not possible on mobile devices without the Flickr app. :(
Since we have ~30 GB of photos it's not really feasible to upload them to our web hosting... ;)