I assume you've already logged in to Flickr and uploaded your photos. So look at a photo, click "More ways to share" to the right of "Actions", then "Grab the link". Hit the BBCode button. Paste that block of text, or at least the part betweeen the [img] and the [/img], and post that code on the forum.
Any link to an image file placed between [img] [/img] tags shows up as a photo embedded in your post.