I encountered this problem with the the HoPE them for Wordpress. I was able to confirm that I'd put in the correct flickr API RSS URL to the Theme Settings because when looking in the page source, I could see the populated values from the RSS feed (look for the "imagearray" variable in the page source). I then pulled down the preview version of the HoPE theme to compare to my own. I did a visual diff of the two and found a few differences. I tracked the problem down to the following :
I had the Lightbox 2 Wordpress Plugin installed and activated on the site. Lightbox conflicts with Simplegallery, the underlying gallery js tool that HoPE uses.
I disabled the Lightbox 2 plugin on the site and the HoPE theme started working.