I've tried naming the file "FlickrService.ss", "FlickrGallery.ss", and "FlickrWidget.ss" as those are the names of the PHP files... I tried putting them in the themes layout directory as well as the flickrservice layout directory (which I had to create), and I can't seem to get it to work...

Essentially, what I am trying to implement is a sub-menu design specific for my gallery pages and a sub-menu design specific for my music pages... Any tips? Learning as I go, thanks in advance for your help!

You don't need to rename anything. Just create an override template in your theme directory. So if you want to customize /flickr/templates/Layout/Flickr.ss, you would create /your_theme/templates/Layout/Flickr.ss. Run a ?flush=1 and you should be good to go.

Perhaps there's some miscommunication... I tried doing just that. It didn't work. I guess my point is that the override template has to have a name matching the page it will override, and I cannot figure out what the page name is. I have tried ?flush=1 and ?flush=all with no luck..