If you have an AmEx card and your deposit amount is within your current credit limit on your card, it should only take a minute or two.
Poker sites that accept American Express deposits have all the proper online verifications set up to have your deposit processed immediately. It’ll likely show up in your poker account instantly but it can take a minute or two sometimes.
If there’s any delay you’ll be able to access the online poker site’s customer support team in real-time and they’ll help make sure your deposit gets through. As mentioned above an American Express deposit may be considered a cash advance so be sure you know what any extra fees might entail.