There may be other reasons for Amazon to team up with AT&T, but surely the retailer-turned-phone maker had updates in mind. Amazon has borrowed from the Apple playbook with the original iPhone that was exclusive to the same carrier.
Neither Amazon nor AT&T are talking about the deal, including how updates will be handled, but it's a safe bet that Amazon wrote controlling the updates into the arrangement. The company already controls updates for its Kindle Fires, and they'll want to do the same with the Fire phone.
Apple insisted on controlling updates for the iPhone from its launch, and that was easier to do with just the one carrier. It removed carrier interference from the OS update equation, a thorny problem for Android phone makers to this day.
A lot has been said about Android updates, or lack thereof, due to having too many fingers in the broth. Apple avoided that with its exclusive deal with AT&T for the iPhone. Once it dominated the smartphone space, Apple was able to include update control in deals with all the other carriers.
Having exclusivity with AT&T will no doubt make that easier to control from the birth of the Fire phone going forward. Amazon will be pushing OS updates to all Fire phones, with carriers out of the process. It's a safe bet update control is addressed in the Fire phone agreement inked between the two companies. Amazon will want to set the precedent for the future, when the period of exclusivity with AT&T expires.
Handling updates is best left in the hands of the OS developer. It prevents outside parties from altering the user experience, and from adding junk software on top of the OS. This has worked well for Apple, and no doubt it will work just as well for Amazon. It will control what goes out and when, and that's a huge improvement over Android.