mike27oct is right. m4a files are just another type of audio file.
But with most digital content, it may be contain DRM protection. Put simply, that means that the file will only play on the device or the account that purchased it. It is essentially locked to that device or account.
For example, you purchased an album on iTunes from your iPad. You can play that album on your iPad. If you copy the file to your friend's iPhone, it will not play. But it could play if you logged into your friend's iPhone with your iTunes account.
That said, if your m4a files are DRM protected, Amazon will most likely reject it because Amazon is not the device or account holder that purchased the content. They cannot be the intermediary that provides the DRM protected content to you, even if you intend to play it back on the device that originally purchased it.
Regarding the topic of DRM, there has been numerous discussions in A/V forums. Personally, I really hate DRM protection. I still have several movies that I've paid for on Google Play, Amazon, UVVU, and iTunes. But I have not purchase any new digital content in a few years now.
One service that I used in the past was Target Ticket. It was a streaming service similar to Vudu or Ultraviolet. They touted that you can watch your movies from anywhere and on any device, provided that you login first. That sounds like a great idea. I can go to my friends house and play any of my purchased movies without having to lug a stack of DVDs with me. The only problem was they shut down in 2013. My movies were supposed to automatically transfer to UVVU but they didn't. It just sat in "processing" for several weeks. At the end of that, it finally showed that I have no content available. So all the movies that I had already paid for just vanished into thin air. DRM prevented me from downloading and keeping my own copy of the movies. So that's the end of the story. Lesson learned. I have not bought any digital content since then.