If your preferred podcast app is Apple's native Podcasts, you can access The Atlantic Magazine in Audio there by following these steps. You'll need to go to the Audio Issues section of your accounts, which you can find how to access here.
Open the Apple Podcasts app on your preferred Apple device.
Tap "Library" in the bottom toolbar.
Tap "Edit" in the top right corner.
Tap "Add a Podcast by URL."
Enter the subscription URL listed in the Audio Issues section of your account.
Head to your library and tap "The Atlantic Magazine in Audio". This should appear under "Shows".
Tap "Available Episodes" to see all articles available.
Add ("+") the articles you wish to listen to (or download them for offline listening!).