These games get added to amazon account? As direct downloads (such as Humble Bundle)? Or Some other way?
If you link your Amazon Prime account to your Twitch account, it will upgrade your Twitch account to Twitch Prime, which will give you access to Prime Loot. There's a Prime Loot icon at the top of the Twitch page. When you click it, it will bring up a list of available free games/DLC. You can then click the "Claim Offer" button, which will add the game/DLC to your Twitch account. You can then download and install the Twitch client, which is similar to the Steam and Galaxy clients, which you can then use to download, install and launch the games. The games are available to claim for free during a 2-4 week window, depending on the title. As long as you add the game/DLC to your account during that window, it will be yours to keep forever.