If your preferred podcast app is Overcast, you can access The Atlantic Magazine in Audio there by following these steps. You'll need to go to the Audio Magazine section of your accounts, which you can find how to access here.
Tap the "+" button in the top right corner.
Tap "Add URL" in the top right corner.
Enter the subscription URL listed at the beginning of the Audio Articles section of your account and then tap "Done".
Head to you library, go to "The Atlantic Magazine in Audio".
Tap "All" to see all the available articles.
Add ("+") the articles you wish to listen to (or download them for offline listening!).