Unfortunately for now this can only work from services hosting all the content. Because podcasts are hosted on their own services/servers, this cannot be done. Hopfully this will change in the future…
An error occurred while saving the commentKyle Houske commented
You can listen to any podcast you'd like using the Amazon Echo by Bluetooth. I haven't been successful at directing Alexa to play any specific Podcast Addict file by speaking to her. It's a matter of opening PA while connected via Bluetooth and using your phones app as normal. The Echo will play the output if that helps.