I just tried the Android Flickr app, and it doesn't have a suitable share option for forums, so I doubt the Apple app will so this needs to be done from a browser.
Log in to Flickr
Find the picture you wish to share and click it, so its the only picture displayed
Down the bottom right you have 4 icons, edit, share, download, and buy.
Click the share button
Click BBCode (See attached)
From the drop down select the size (See attached)
Finally copy the code from the box.
Paste it directly in to your forum post, it is already formatted with IMG tags, I just remove the last URL as it makes things untidy.