I know that Chris Lester’s Metamor City stories frequently have furry characters and he records them as podcasts before publishing them on Amazon.
Though, given that he self-publishes, as Liminal Corvid Press, I expect he doesn’t have any legal issues that authors who have others publish their works.
Income from podcasting, so far as I can tell, would be sparse, probably limited to Patreon or similar donation schemes. I don’t know if you’d be able to convert podcasts to Audible audiobooks. Still, if you’re already posting stories on SoFurry for free it probably wouldn’t hurt to Podcast them, help promote your works I suppose. I did record a story of mine as an mp3 and put it on my galleries just to see the response http://www.furaffinity.net/view/20190263/