Changing the privacy settings on your Flickr account (or even deleting the account entirely) will take a bit of time for your content to be removed from search engines.
Search engines re-index the content that appears on their site on their own schedules & when that re-indexing happens, your updated content will drop out of their search results.
Note - This may take some time and is solely in the hands of the third-party search company, and falls outside Flickr's control.
Some search engines allow you to request removal from their index. Check out these links for further information: