How to remove your Flickr account
Be logged in, use the removal link. Of course, your linked Yahoo account won’t be removed. However, if you delete your Yahoo account, your Flickr account will be removed as well.
Direct removal link: http://www.flickr.com/account/delete/
Helpful Trick: Removing online data
Helpful Trick: Remove third-party logins
If you signed up for Flickr using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Flickr. Click here to find out how.