Amazon HD is basically lossless 16-bit FLAC, so in principle the same as local 16-bit FLAC and better than lossy MP3.  The sound quality does not depend on whether local or internet source.  

Whether you can actually hear any difference is another question, and depends on your hearing, the track being played, which Sonos speaker is being used, room acoustics….

Thanks - based on your answered I searched at Amazon and found 

HD tracks are 16-bit audio, with a minimum sample rate of 44.1 kHz and an average bitrate of 850 kbps 

 Ultra HD tracks have a bit depth of 24 bits, with sample rates ranging from 44.1 kHz up to 192 kHz, and an average bitrate of 3730 kbps.

So I just compare the format of my local file and compare it to this and the higher “spec”ed one is better.

although would probably agree that using a Roam in my room at home, I may not notice the difference.

One advantage of adding my home collection on to the Sonos app is it made me clean up the Artist names in my mp3 files, after seeing the horrible mess my tags were :) 

I can’t hear any difference between local FLAC and amazon HD when played on a pair of Play:5 (gen 2) + Sub, and I don’t think anyone would in a blind trial.

What’s the bitrate of the local MP3 files? MP3 is an ancient codec, with audible compromises especially at low bitrates.

https://www.soundonsound.com/techniques/what-data-compression-does-your-music

Hi

Bits and Piece’s aside (pun intended)  The Roam which uses Auto-Trueplay may not be the best Sonos speaker to determine audio quality comparing relatively closely match formats (may be with the exception of MP3). Your ears will adjust accordingly and most likely deprive you of a serious A/B/C comparison. This also previously alluded to by @John B.

On a small portable speaker like a Roam you will hear no difference.  In fact I can’t even hear a difference between 256 AACs and the same “Ultra HD” files streaming through my Sonos Port to a 3,000 dollar Denon and Aperion Audio sound system. “Hi-Res” audio is seriously overrated, especially given most people don’t spend that much on their playback equipment.

If you want better sound quality the best thing you can do is get better quality/larger speakers.  My Sonos Move is nice enough but it really can’t touch the Sonos Ones I have paired to a Sonos Sub and the Ones/Sub combo in turn really can’t touch the Denon/Aperion system. And these increases in sound quality are occurring with regular old 256 AAC streams.