Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
I would advise you to sign into the flickr account with the flickr password.
If that does not work, then you may need to sign in to your Yahoo! account first - and if already signed into the Yahoo! account, sign out of it first, restart the computer, and sign in to it - and then try the flickr account sign-in again.
Also... ultimately, you may need to test signing in to Yahoo! directly. In case it is the Yahoo! password ***** is not working.
And if that works and you get to this point, but the flickr account still won't sign in - then, try the 'Forgot password?' or other password ***** option that the flickr sign-in screen shows.
Let me know how it actually goes, and what you find out, and I will advise you additionally as needed.