I have been having trouble signing into flickr for a long time now. As a matter of fact, I mostly stopped using flickr because of this issue.
My initial tests pointed to a third-party cookie issue. It seemed that either flickr was requiring them or Opera was misinterpreting non-third-party cookies as though they were third-party cookies.
A recent test has shown this to be incorrect. The problem does relate to the cookies but in the end you will be able to sign into flickr with third-party cookies globally disabled using Opera.
Here is my workaround. It is very simple.
When you attempt to sign into flickr you will be taken to a page showing this:
Clicking on the login link or returning to flickr’s home page and clicking the login link or just going to the login page directly will all take you into this silly loop from which you will not be able to extract yourself.
What you may not notice is the small redirect page which flashed just before this cookie error page. Go back one page (using a keyboard shortcut, a mouse gesture, or your browser’s back button) and you will see a page which reads:
If you are seeing this page, your browser settings prevent you from automatically redirecting to a new URL.
Please click here to continue.
You have successfully worked around the issue. Congratulations.