Two things you may be doing wrong.
-Using the "html" code on flickr instead of the "img" code.
-Special bbc code icon? Do you mean the image button, the little square picture under the smiley face?
Heres how it works when I do it. I have photobucket but they should be the same.
-Have two tabs. One on THP and one on flickr.
-Find the pic you want on flickr.
-If the pic has a share button, click it.
-There should be three codes to use. HTML, E Mail, and Image.
-Use the IMG code to right click copy or highlight and copy.
-Go to THP tab.
-In the reply box, find the left most clipboard icon on the top row.
-It may ask for access to your clipboard, click yes.
-It will automatically paste.
At first you wont think it worked, because it just shows the text. But when you post it will be converted.
That should be it. Give a try and see what happens.
And a tip if you plan to use an internet image:
-Right click the image and select properties.
-Highlight and copy the URL code in the properties box. It should end with .jpg
-This time click the square image icon under the smiley face in the reply box.
-A box should appear.
-Paste your URL. This image should be immediate.
Some internet images cannot be copied, make sure they end in .jpg. Also, some URL codes are not entirely visible at first. Again look for the.jpg file extension at the end of the URL. To make the full code possible you have to look when you are highlighting it. I highlight from the bottom up.
Happy posting.