Here's how to do it:
1. In Flickr, open the picture you want to show by clicking on it.
2. Select 
Share and 
Grab the HTML/BBCode.
3. Select a suitable picture size, not too large, and tick the BBCode box.
4. Copy the code that shows up in the window.
5. In the Trainz forum thread post, paste what you copied. It should show up as text.
6. From what you just pasted, select and copy the URL for the picture (something like 
http://farm9.staticflickr.com/1234/567890_etc_etc.jpg).
7. At the place in your post where you want the picture to appear, select 
Insert Image from the list of icons above the post text. Paste the URL into the window that opens.
8. Remove what you pasted in step 5.
(The reason for the extra edit in steps 5-6 is that Flickr adds some extra info, such as a link to your Flickr page, that you don't necessarily want to include.)