Here is how you can get 3 months of Amazon Music Unlimited for free

The first one is to be a new subscriber, which means you shouldn't have benefited from another trial in the past. Obviously, if you're a returning subscriber, you don't qualify for the deal. The second requirement is to purchase an eligible item shipped and sold by Amazon and either sign up for an eligible Amazon subscription (Prime, Kindle Unlimited, Prime Video Channel) or register an eligible device in the Alexa app.
If you meet these criteria, you will receive an email from Amazon with instructions on how to redeem your three free months of Amazon Music Unlimited. The offer is only available in the United States and you have 30 days to redeem it.