How to claim Apex Legends Twitch Prime loot
If you are a Twitch Prime member, you will need to head over to the official offer page here. Once you've signed in, you'll need to link your accounts - you can use this link to link your EA account with Origin/PSN/Xbox Live. If you've already linked your account, your rewards will be there when you sign in!
You will also receive a notification on the top bar of the Twitch website (on desktop), where you can find all Twitch Prime loot.
The Twitch Prime pack was announced during the 2nd Twitch Rivals tournament on February 19, which you can keep up to date with here.
Presumably there might be more Twitch Prime packs in the future for Apex Legends, so make sure you have everything connected up if you want some free content.