Flickr is using a secure authentication method made possible by the new Blogger’s use of Google Accounts. When you want to add a Blogger beta blog to Flickr, Flickr will redirect you to google.com to enter your username and password. Read more about granting access to websites.
Flickr (and other websites that support this technology) will never see your username or password; all of that information is kept securely on Google’s servers. In addition, these websites will only be authorized to post to your Blogger blog. They will not be allowed to access your seach history (if you save it, that is), your Gmail, your Google Checkout data, or any other part of your Google Account. If you ever want to deauthorize a website and disallow it from posting, you can revoke its access from your “My Account” page.
Remember, never enter your Google Account login information on a website not owned by Google!
