Here is a briefing about Amazon Prime refund policy. There are four conditions for cancelling Amazon prime subscription.
Cancelling within 3 business days of signing up for free membership:
If you cancel a prime membership free trial within 3 business days, you get a full refund. However, Amazon will charge you or withhold from your refund the value of prime benefits you use in these three business days.
Cancelling any other time: you get a full Amazon Prime refund Policy, if you did not make any purchases or access to prime benefits since your sign up.