When you Pay with Points, the full cost of the flights is charged to your American Express card, and then points are redeemed to offset the cost. This means that BA sees this as a simple cash purchase made through a travel agency. I wouldn't focus on the points, what you want is a refund of the money.

Be aware that American Express Travel (USA) is operated by Expedia. Most likely you are dealing with Expedia employees.

Can you find your reservation on ba.com? (You need the BA record locator, which may be in an email that you received from Amex Travel or BA at time of purchase.) Has it been cancelled? Amex Travel won't refund the transaction until BA issues a refund.