You don't have to set an American Express travel notification under any circumstances. Amex is one of the few credit card companies that doesn’t allow it. Most issuers want you to tell them ahead of time when you plan on traveling, so they won’t flag your purchases as fraud if they see you spending money in another country or state. Amex, on the other hand, is confident in their ability to recognize fraud without travel notifications.
This is what American Express has to say about travel notifications on their website: “We use industry-leading fraud detection capabilities that help us recognize when our Card Members are traveling, so you don't need to notify us before you travel.” While the exact nature of how they do this is an Amex secret, some Amex customers have been able to provide insight into the process. For example, some report that Amex sent them an email saying their recent purchases indicated they’d be traveling in the near future. So if you buy plane tickets, for example, Amex will reasonably assume you’ll be going somewhere.
So in the end, you don’t need to set an American Express travel notification, and there’s no way to do it even if you wanted to. You should just expect Amex to figure out when you’re traveling. But if your card ever is flagged for fraud, a call to the number on the back of your card should quickly sort things out. It’s also a good idea to make sure Amex has the right phone number on file for you, so they can let you know if there’s an issue.