I'm thinking you would have to hard code this into each affiliates site, which would be easy if you only had a few, but if you have a lot or plan on getting a lot, then Listmail really isn't where you want to run your affiliate program from.
I'd suggest getting an affiliate script of some sort that makes doing things like this easy. I can't suggest any off hand, but I'm sure doing a search would get a lot of results.
On the other hand, doing it quickly for just a few affiliates would be easy. Just Create a list, make affiliate_ID a field, then on the form on each affiliates site just hard code that affiliates ID into the form like this:
<form method=post action=http://YOURDOMAIN.com/listmail/signup.php>
<input type=hidden name=list value=1>
<input type=hidden name=affiliate_ID value=YOUR AFFILIATES ID>
First Name: <input type=text name=fname size=10><br>
Email: <input type=text name=email><br>
<input type=submit name=sup value="Subscribe Me!">
</form>
Then on all the follow ups just point the URL's like this:
http://www.yourdomain.com/!affiliate_ID/
Should work, test yourself before implementing this.