Others on Amazon's forums report the same thing. I guess we need to wait a bit longer for Amazon to get things ironed out.
no love from Origin yet
Thank you for ordering Battlefield 3™ Limited Edition from Origin. The game is now available for pre-load. To begin, please follow these steps:
Launch the Origin Client and login to your account.
Click on the “My Games” tab and find the Battlefield 3™ Limited Edition icon.
Click “Ready To Download” and follow the prompts to download the game.
On October 25, 2011, you will be ready to play when Battlefield 3™ Limited Edition releases.