Click on 'all sizes' above your photo of choice
and you are taken to this page, which has your image plus several prepared links you can copy and paste. TeaChat and most forums only work with the second one, the long string of characters:
What I circled up top was the large size, which is the wrong size for TeaChat--it's better to click 'medium' and to use the link from that page, because it will be the right size (no more than 500 pixels in either dimension). Select the entire link, copy to your clipboard.
Open a reply in TeaChat, click the Img button on top of the post box, and in between the two pairs of 'Img' in brackets, paste your link.
You're done. Yay!
If you want to see these screenshots full size, click here:http://www.flickr.com/photos/debunix/sets/72157600046070357/