I’m having the same problem as well! However this may not be immediately fixable in the plug-in.
It looks like Flickr is making some major changes to the security for it’s APIs. See flickr-api-going-ssl-only-on-june-27th-2014. The rollout of this change will include some backout dates on June 3rd and 17th.
According to the link above by flickr, existing API keys issued before May 6th will continue to work against both the old http and new https REST APIs. At least that’s what they say. API keys issued from May 6th on will only work against the new https REST API.
It also seems as if miro.mannino, the developer for the Flickr Photostream plug-in is pro-actively updating the plug-in to accommodate this change by Flickr. As such the 3.1 update is now using the new https REST API. In theory this should be working for both old and new API keys. Unfortunately this does not appear to be the case at this time. I’m not sure if it’s a problem with this plug-in or with the current state of the flickr APIs.
While this is definitely affecting my website, I expect there to be some disruption while miro.mannino attempts to keep pace with the changes being made by flickr and the lack of stability in those APIs.
Hopefully flickr will figure out their issues and miro.mannino will release any required updates as soon as possible.