I've been worried about Flickr disappearing for a while, but I don't think it's anywhere close yet. Also I'm not really interested in yet another third-party service from someone even less trusted than Flickr.

I'm happy to see projects like parallel-flickr pop up. I even started my own version: https://github.com/aaronpk/Flickr-Archiver

There are few things I trust more than Flickr right now, but I want to be ready in case they sink in the near future.