Note that Amazon affiliate marketing (which I'm fairly certain, though not 100% positive, this is part of) is complicated in how it allocates the purchase to the affiliate. If you saw a website/video and clicked on someone else's sponsored link to get to the product page on amazon, it doesn't matter if you do a 'put it in my cart, take it out again, click on the link' cycle - the original referrer will get credit, not Jetblue, if you buy it within 24 hours. In some cases, for high value items, it's not just 24 hours - it's up to 90 days. Google [amazon 24 hour affiliate cookie frequently asked questions] for the extensive discussions people have had trying to figure out how exactly this works.

If you want to make sure you're getting every penny - never click on a link that leads you to Amazon, and do not stay logged into amazon - only open it in a separate incognito window when you're ready to make a purchase, and make sure to get to the item by doing a search within Amazon, after clicking the jetblue link.

An easier way to get cash back from Amazon is likely just to use one of the many credit cards (e.g, Chase Amazon Rewards Visa) that gives you a fixed percentage back, regardless of any affiliate marketing.