To share the images on your Flickr account, you first need to enable sharing.
Follow the following menu path on your Flickr Account:
You> Your Account> Personal Information> Privacy and Permissions> Allow others to share your stuff?: Yes.
Then at the top of your image you will see sharing buttons for Email, Facebook, and Twitter. Click the dropdown menu that says "More ways to share" when highlighted next to the Twitter button.
The box that appears should have the option to "Grab the HTML or the BBCode" for the image. Check the BBCode box, select your size (medium 640 is good), and copy the code that appears there (which will begin with the [ img ] tag, if it begins with the < a href:" > tag you have got the HTML) then paste that into your post on the forum. The code provided will insert the image into your post, along with a link to your image and flickr account.
The code looks like this:
[url=http://www.flickr.com/photos/busterbeam/5787134973/]DSC07550[/url] by [url=http://www.flickr.com/people/busterbeam/]Busterbeam[/url], on Flickr
and what is displayed on the forum is this:
, on Flickr
If you are having trouble finding the BBCode, perhaps the user has sharing disabled?
Otherwise please post any questions or concerns regarding Flickr in this thread.