In the chart of accounts, how should American Express Working Capital Terms Program be set up? Specially since they make payments directly to vendors.

It could be argued that this constitutes a "third party payer" and that Amex is responsible for issuing 1099-k to your contractors https://www.irs.gov/payments/third-party-network-transactions-faqs but that answer may be beyond our expertise since it is ultimately a tax question. If your accountant is your tax CPA they may be correct.