Do you mean you don't want your Flickr acct and the photo title appearing beneath it? The code Flickr generates looks like this:
[ url=http://www.flickr.com/photos/whenigodeaf/6441625281/ ][ img ]http://farm8.staticflickr.com/7007/6441625281_409bd47065.jpg[ /img ][ /url ]
[ url=http://www.flickr.com/photos/whenigodeaf/6441625281/ ]ERIE[ /url ] by [ url=http://www.flickr.com/people/whenigodeaf/ ]QsySue[ /url ], on Flickr
Except without any spaces. To leave out the link to your account the title, remove everything after the first closing url tag: [ /url ]
So it just looks like this:
[ url=http://www.flickr.com/photos/whenigodeaf/6441625281/ ][ img ]http://farm8.staticflickr.com/7007/6441625281_409bd47065.jpg[ /img ][ /url ]
If you don't want the image linking to your flickr at all, then remove the url tag from around the img tag, so it just looks like this:
[ img ]http://farm8.staticflickr.com/7007/6441625281_409bd47065.jpg[ /img ]
Except without any spaces. I had to put spaces in the tags so they'd show up on the board rather than embedding the image.