Firefox's Web Console lists numerous errors (at least one for each image) referring to the site's Content Security Policy (CSP). Since the requests are made through Flash, I'm not sure how to diagnose that further, but one workaround would be to temporarily set Firefox to ignore the site's CSP. This reduces your protection against alien scripts possibly being run by the site, so it's a good idea to turn it back on again when you are no longer experiencing this problem.

Screenshot attached for comparison.

Here are the steps:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful.

(2) In the search box above the list, type or paste .csp and pause while the list is filtered

(3) Double-click the security.csp.enable preference to switch the value from true to false

I think you'll need to reload the viewer and then it should work.

When you're done, you can double-click security.csp.enable again to switch it back to true.

If you are a regular Flickr user, could you report this problem to them?

Today I was able view the slideshow in Flickr running on FireFox. Thankfully, I no longer need to use the temporary solution provided above.