Just a heads up regarding the latest version of the app. It doesn’t provide cross device syncing yet, but it allows you to sign in to your Google Drive account and have all your data automatically backed up to make sure they are safe at all time. It also makes restoring the data on a new device really easy.
You can go into Settings/Backup to enable this and sign-in
An error occurred while saving the commentTomas commented
Just commenting, I've switched to Pocket Casts due to this. But I'm not totally happy, if you implement it, I'm coming back and donating.