How to listen to music on Apple Watch se

Amazon Music is not an Apple product, best you ask the app developer on their website/forum for support.

For Apple Music:

Add music using your Apple Watch

If you’re an Apple Music subscriber, you can add music using your Apple Watch.

1. Open the Music app  on your Apple Watch.
2. Tap Library, Listen Now, or Search, then navigate to music you want to add.
3. Tap a playlist or album, tap , then tap Add to Library.
4. A message confirms that the item was added.
5. Note: You can stream music you add to Apple Watch when you have an internet connection. To play music when you’re not connected to the internet, you must first download it.
6. To download the music to Apple Watch, tap  again, then tap Download.
7. Music is added when Apple Watch is connected to power and Wi-Fi.