[wrxtasy]

OK,

So I only need Dolby Digital and not DD+, are you saying that only the ATV or Amazon fire can down mix to output DD only?

Yes

How about the nvidia shield? Can this provide DD from Netflix?

No DD+ only, you need a DD+ audio receiver for 5.1 DD+ Android TV Netflix audio.

So if I go with an Amazon firestick, what are the main things I'd be missing out on?

I would not use a FireTV stick for demanding Kodi usage.
It is the last device you should be looking at for Kodi usage.

Auto refresh switching will not work and Kodi DTS audio support will likely be spotty or not work at all. I doubt 7.1 passthrough audio would work at all, the FireOS Firmware simply does not support such Kodi audio bitstreaming I believe.

You are going to have to compromise or buy an Apple TV 4K that has much better legacy AVR DD only and 5.1 / 7.1 LPCM audio support.
Then you would use the MrMC App, but it has Addon and Skin limitations, you cannot self install extra ones to what already come packaged with that App.

Your DD only AVR is what limits your hardware choices.