Saw this offer on my account and then today got an email as well. Looks like this in the body of the message...
Now through May 19, 2019, get a $3 promo code when you listen to a full song on Prime Music for the first time.
The code will be emailed to you by May 26, 2019 and can be redeemed until May 31, 2019 on an eligible purchase of $15 or more. Terms and conditions apply.
Prime Music is an included benefit of your Prime membership. Listen to over two million hand-curated songs, plus thousands of playlists and stations online, on an Amazon Echo device, or on your mobile device with the Amazon Music app. Enjoy music anytime, anywhere -- at home, the office, the gym, or on-the-go.