https://www.americanexpress.com/icc/Note that Amex accepts payments from third parties for settling the account balance, you just need to indicate the card number in the payment narrative.
Then you'll probably not be able to get a business Amex, unless you have a lot of cash and can get private banking status with one of the major banks. You can of course try applying with banks and see what happens. But be careful about running too many credit checks. It can start to reflect poorly on your company.
You might be able to get a personal Amex from a US bank if you manage to open a personal account and can show you already have a credit card with a decent limit (10,000 USD or above). Will likely have to be done in person.