I guess the odds are that you're not all running the same browser.
By intermittently, do you mean that given a particular post,
you sometimes see the image and other times get the Flickr error message? If so, interesting, and points to Flickr as the likely cause. I suppose there is a small chance that browsers could be mis-communicating with Flickr, or the request is being corrupted when sent to Flickr, but I have my doubts about that.
I've seen that error in the past too (on Safari up & down the Pacific West coast). In the end I just decided to ignore those posts. I can't fix Flickr and I'm not going waste time trying to back track the link or refreshing the page. The error suggests a possible temporary problem, so maybe I'll be lucky to see the image on return to the daily thread.