Not sure if it will work HDMI
TO Cinema Display's Mini Display port but you might try
this dongle. That might only work the other way Mini DP
TO HDMI. In other words, it might only work ONE way (conceptually old Mac to HDMI display instead of HDMI anything to Display Port hardware). Why? Content protection. A key part of HDMI is to prevent copying of content and I can't recall if Display Port has good support of "end to end" content security or not.
As to audio, Cinema Displays did have speakers, so if it works, you should have sound too. Else, you might want to get a little A/V amp or receiver with HDMI jacks and some "dumb" speakers.
Firestick HDMI into AMP:
- HDMI OUT of AMP to Dongle to Cinema Display.
- AMP speaker terminals to "Dumb" speakers via speaker wire.
But first, you better see if you can get HDMI TO DisplayPort working from Firestick. It may not. My best gut guess is that it will
NOT work but maybe someone else will chime in with a success story.
Else, small, off-brand HDTVs can be purchased for < $100. Between the money for the fire stick and a dongle, you might have 30% of so of the price of one of those $100 televisions, some of which will have at least mainstream video apps on board
like this one or
this one or
this one. $100 TVs will NOT be spectacular televisions but you'll get a picture and sound with no hack/dongle requirements and security complications.
If the TV idea appeals, another option might be to go
cheap projector for a bigger "screen."