No, wasn't a stupid question at all. Not many people on the dev team actual uses the module so bugs like this are often not looked at. The file that I believe you would need to edit is the Paginate function in FlickrService file - http://open.silverstripe.org/browser/modules/flickrservice/trunk/code/FlickrService.php (FYI this does it a really bad way so don't learn anything from looking at the code) which returns the html for the pagination.
Looking at that code quickly I see the code for prev / next is in that file but I see it refers to a $current_page variable which doesn't look to ever to set. You might want to debug lines 212 in FlickrService.php till line 238 to see what if anything is wrong. Try Debug::show($currentPage); Debug::show($last_page) etc to see what variables aren't being set and why the buttons aren't showing. Since it looks like I've been assigned the module I'll try it out and see if it works for me and what the solution is.