Buy Amazon Prime with your card and you will automatically get a $79 statement credit to cover the cost of Amazon Prime for the first year.
You must be a new prime user to qualify and you need to sign up within three months of being approved for the American Express card. You also need to spend the amount necessary to collect the sign up bonus to qualify (ie - $1,000 on Blue everyday within 3 months)
Sign up for Amazon Prime from these sites:
AMEX Platinum Sign up
AMEX Blue Cash Preferred Sign up
AMEX Blue Cash Everyday Sign up
AMEX Enhanced Business Gold Sign up