Unfortunately, nonstop flights aren't an option between Dallas, TX Airport (DFW-Dallas-Fort Worth Intl.) and Amman Airport (AMM-Queen Alia Intl.). However, there are several carriers that service this route with just one simple stopover, including American Airlines, Qatar Airways and Emirates.
With a minimum flight duration of 13 hours and 20 minutes, it's a wise idea to be as comfortable as possible. Racked up a few air miles? You might like to use them to upgrade your seat on your Dallas to Amman trip.