You initially buy the flight with points. It is not a statement credit like other programs work. So you would either call or use the site to book, your credit card wouldn't be charged the cash nor would you earn 1200 points, as you didn't pay for the flight.

To pay with points often is a bad value of points. That $400 flight would cost you 40000 Amex points.(32,000 if have Plat/Cent) Continental isn't a great example as they are no longer a transfer partner, but if a low award is available on that flight it would have only cost you 25,000 Amex points transferred to the airline.(Even less if the airline is running a transfer bonus.)