How to get a media.textadventures.co/uk link?

After publishing your game, click on the "Play" button.

That takes you to your game on media.textadventures.co.uk.

Is that what you were looking for?

Oh, I mean like an image or sound file

If the file is inside your game, the link should be the same as the one for the game itself.

So if you play a game and it gives you an address like:

http://media.textadventures.co.uk/games/tvbRARoUSES9Gs0xJLNPjg/index.html

any images which are inside the game's zip will be accessible as:

http://media.textadventures.co.uk/games/tvbRARoUSES9Gs0xJLNPjg/imagename.png

This means that in most cases, you can use a relative URI (just the filename).
I've not really played with this, as I haven't got around to installing the desktop version yet. But I'm sure someone who has it can help you.