No Dolby digital from Amazon video
I Get DD audio via Netflix, but not from Amazon video.
amazon claims they are sending DD, but only receive PCM audio.
Using ATV, iPad, AirPlay.
Let's start with which exact generation of the Apple TV do you have? I am going to assume it's the (current) latest, generation 4. If so, I am not aware that Amazon has released their Video app for this device ... so, it begs the question: Where are you streaming Amazon content to your Apple TV? I'm guessing from your last sentence it's from your iPad's Amazon Video app via AirPlay ... correct?
If this is correct, then the answer can be found at the following Amazon support site. Amazon video does not support 5.1 audio on iOS devices. Since there is no digital multichannel audio available, the iPad will compress the digital stream in Apple Lossless, encrypt it, and then, send it to the Apple TV. In turn, the Apple TV would first decode the stream, and then output raw PCM to your HDTV via HDMI.