First, you need to have a Twitch Account and be a Twitch Prime member. If you do not have an account yet, you can create one on the official Twitch website.
If you would like to know how to turn your Twitch Account into a Twitch Prime Account, have a look at this Twitch Guide.
Getting your bonus content is easy. Just go to the Twitch Prime website, find Assassin's Creed: Odyssey on the list and click Claim Offer.
You will be redirected to a Ubisoft website and prompted to log in with your Twitch Account. This will link your Ubisoft Account and your Twitch Account.
Next, you will be asked to choose the platform on which you want to receive the content. Please make sure to select the platform on which you play Assassin's Creed: Odyssey as the offer can only be claimed once and is not transferable to other platforms once redeemed.
If you have not yet linked that platform to your Ubisoft Account, you can do it from here by clicking on the corresponding button.
Click on Get My Gift. This will finalise the process and the bonus content will be granted to your Ubisoft Account and the platform you selected.
When you start Assassin's Creed: Odyssey the next time, the item should be available for you in-game. Please navigate to Store > Owned and claim the item from there. It should then appear in your character's inventory.
If you encounter any issues with the Ubisoft website, please feel free to contact us. For all issues you may encounter with Twitch, we would like to ask you to contact Twitch support.