[OtinG]

Recording shows, even just the audio, is usually forbidden under USA law without the express permissions from the owner of that media. I would think that is also true in most countries. So I doubt you will find an easy way to do it because Apple probably has at least tried to prevent those kinds of unauthorized recordings. After all, Apple gets paid to stream those shows/podcasts and likely has some strict contractual agreements with the media owners, as do cable, satellite, and other streaming companies. There might be some 3rd party apps that can do it, at least until Apple catches on and bans them. But I wouldn't hold my breath.

Your best bet might be to use a second device to record the podcasts off of the first device, but that would mean using the microphone on the second device to record the sounds emitted from the speakers on the first device, so quality won't be as good. A cheap digital recorder would work, or of course another iPad, iPhone, or computer.

Disclaimer: I don't recommend making unauthorized recordings of any kind. However, what you do is none of my business. Such recording considerations are between you and the media owner(s).