When you take up the Airtrain offer of free travel from airport to Bris during Feb by flashing your FF Card, they hand you a form which you can fill out and either fax, post or email back to them.
The form is similar to this one:
http://www.airtrain.com.au/ktml2/fil..._OrderForm.pdf except, it has $5 per ticket, and a statement down the bottom "Discount offer valid for orders until 28 February 2005. (Tickets valid through 2005)"
If you trust your CC details over email (I don't!) then you could email them and get it that way. Otherwise, find a form and fill it out.
If you aren't near the airport and need cheap tickets from Bris city to airport, find one of the locations that sell the $8 airtrain tickets. Most of the touristy information places, a few travel agents and some internet cafe/backpacker hostels sell them.
(Oh, and Airtrain are pretty quick with posting the tickets out ... sent letter Mon, received tickets via registered mail on Wed morn)