A quick mono app hacked together to extract the refresh-token from the Amazon Drive desktop app and use it to get a valid bearer token.
Will probably break when the app updates as it has a hardcoded initialization vector in the source file. My guess is you don't need to ever run the app again after the initial login but the code is fairly complex and I've only spent an hour investigating this.
No idea what Amazon would think about this use of the app but since it's an oauth token issued to me for uploading to my cloud drive it's probably not that much of an issue. Happy to remove the gist if there are any concerns.