Ok so I've done a little bit of research into this, and I have come to the conclusion that it's pretty tough to make it in the world of spoken word poetry and audio recitations.
Firstly, the platforms:
The two that I kept seeing mentioned were http://www.audible.com/ and http://www.acx.com/ - both of which are owned by Amazon.
Spotify, ReverbNation, iTunes and all the other music platforms are possible too, but the two Amazon-owned platforms made sense because they are specifically geared towards spoken word and audiobooks.
Marketing yourself
The most difficult part about making a career (or earning any money) out of your spoken word endeavours is that, unlike the music industry or traditional publishing, the audience size is considerably smaller.
So, even though indie bands and authors also struggle to establish themselves, at least they have the realistic possibility of a record label or a book deal at the end of the tunnel.
For spoken-word artists and poets, that chance is more remote, and even successful artists often have to rely on a second source of income.
And to reach a sizeable audience, you'll need to be business-savy, computer literate, entrepreneurial and very dedicated: A one man/woman marketing machine essentially!
However, in my research I did find some interesting characters.
First up is Marc Marcel with his take on how to sell spoken word CDs. His approach is somewhere between rapper and comedian, and I think it works really well.
The second story I came across was of "Queen", a former Crips gang member who has reinvented herself as a "poet/actress/dancer/writer of slogans"
You can read more about her adventures as a spoken-word artist here.