Once Swagbucks finish processing your gift card (usually takes 2 weeks for Amazon Gift Card), you will get an email looking like this.
Just click the "View My Gift Cards" button to be taken there.
If you think you have missed the email, you can track the status of your orders by clicking the "My Account" link right above the "Account Summary" box at the top right corner (kinda).
To find your gift card codes, go to "My Gift Cards".
If you need help redeeming an Amazon Gift Card, please see the blog post here.