Oh yes... I forgot that was a thing. Its been a few years since Ive created the account. When I first signed up, Facebook and Google login werent an option. I created a Yahoo email with the same info as my regular email and used that to sign up for Flickr. Ive only logged in once to that email and that was to verify my Flickr account. Then you just log in normally. It was a minor inconvenience for all of about 2min 8 years ago. Going strong still and no email issues to date.
You are correct though, Im not sure why Flickr does signups that way. Weird.