I got the card today for the $70 sign up 'Gift Card', only have 2 other credit cards with $5,000+ limits with $0 balance on both and want to know when I can close the Amazon account. I only spent .70cents on it so far and want to know if closing it within a month would negatively impact my credit score? Should I instead keep it open for a year at least then close it, keeping a $0 balance the entire time?
Based on the situation you describe, I do not think there is an advantage to waiting a year. The act of closing an account affects your score because important inputs include (1) how much unused credit you have available (2) how many accounts you have open (3) the average time-length of your open accounts. All of these are of high importance and will be affected when you close the account.
However, once an account is closed, in good standing, it will have little or no effect on your score (the details of the credit score algorithm are proprietary). If it does have any effect, which I doubt, the algorithm will most likely not care whether your account was open for a month or a year before it was closed.
If you are interested in maximizing your score, as I'm sure others have told you, your best bet is likely to leave the account open. It will reduce the average age of your accounts (bad) but it will help your utilization and the number of accounts you have open (good). You can use a credit simulator like CreditKarma to get an idea of which metric is more important in your case.