Closing a card has a negligible (if that) impact on your FICOS. The main way it can hurt you is by lowering your total available utilization. This won't matter to you anyway, since the AmEx is a charge card.
I say close it if you don't use it. It doesn't hurt your Average Age of Account (AAoA), because the card stays on your report for sometime. By the way, don't pay attention to CreditKarma or sites like that. The scores they give are not FICOS.