I've seen this recently after doing a factory reset on my phone - though when I then later restored my old data partition (where Flickr was already authorized), it worked fine.
In other words, the issue has to do with loading the authorization URL. I tried copying & pasting this URL into the standard "Internet" browser -- it turns out the page
does exist, however there is a certificate error when attempting to load it. It seems that the CA (Verisign Class 3 Public Primary Certificate Authority - G5) is not recognized by Android out of the box.
I've added this CA to my phone (Using Firefox on my desktop, I exported the certificate to a ".cer" file, copied to my phone, and then installed via
Settings -> Security -> Install from phone storage) -- and now all of my phone's browsers (the default "Internet" browser, Chrome and Firefox) all load the URL without any warnings.
The bad news is that this did not seem to make any difference for the original purpose - to authorize "Flickr for HTC Sense".
Perhaps it's using its own CA store?
Still looking into it...