This is seriously a usability disaster. I have to go through the normal Amazon store to add music to my prime library? I have to leave the player to find music to listen to? No thank you.
Additionally, the player URL (http://cloudplayer.amazon.com) prompts me to install Flash, something I've been unwilling to do for years now.
You don't. cloudplayer.amazon.com -> type in search -> look at right-hand side.
I can't fault free new music, but this interface feels like it was poorly bolted on to a retail sales website, which is exactly how the web video service has always felt.
Edit: I just realized that 3 of the albums are in the search results. I turns out the right tab is scrollable, and after 15 items, it switches to showing matching albums, which includes 3 of the 4 Daft Punk albums, and also some Macklemore.