So here's how you do it: The prop is being given away as part of the Chain Reaction deal inside Microsoft's "Sales and Specials" app, which is a free app designed to point you toward games and content on sale. If you don't have this app, you'll have to download it – go to the Games tab on Xbox Live, and then choose "Browse Games." The "Sales and Specials" link is up in the top right corner (it currently features a Madden 2013 graphic), and then you'll just need to click on "Get the Free App" to download the app. It'll update once if you don't have it yet, taking up about 150 MB of hard drive space.
Once you have the app, you can simply navigate over to the "Chain Reaction" set of deals, and the first deal in the chain is a free biplane, no strings attached. Sure, it's a little complicated, but the holidays are over, right? Might as well pick up one more present while you can.