Unfortunately you cannot install it on flash memory sticks, like you have mentioned you have to install it on a specific Hard Drive for the Xbox 360 Slim/4GB.
Need for Speed Rivals Xbox 360 Installation Information
Need for Speed Rivals on the Xbox 360 requires an Xbox 360 Hard Drive with 3GB of storage space for a mandatory installation of game disc content. you will be prompted to perform this installation the first time time you boot up your game.
You cannot play your game without this installation, nor can it be installed on flash memory sticks, or internal flash memory--such as the internal memory of the Xbox 360 Slim, or 4GB model.
Hard Drives are available and sold separately for the Xbox 360 Slim/4GB, Arcade, and Core consoles.
