Affiliate links and sponsored posts have been the only way to monetize Kinja. In my exchange with A.J. Daulerio regarding Ratter, we touched upon the fact that an alternative revenue source would have to be developed for sites built upon the platform and by all appearances, they're beginning to experiment with the idea.
Sometime recently, the two Hearst publications on Kinja have had Google/DoubleClick ads added to their pages in the same spots the Gawker sites use. (Cosmopolitan, Road & Track) The same has been added to the Playboy Kinja within the last day or two. Because I'm not privy to Gawker Media's internal discussions, I don't know if the DoubleClick ads are their only option or if they will be able to sell the ads and use Adsense as backup, like the Gawker Media sites do, but this is a change from what had been. (I also don't know if there's a split on the income. My gut says there's not and it's all going to the magazines, but I don't know.)
Kinja has reserved the right to put advertising on our individual blogs and/or communities. Perhaps that's coming or maybe it'll go the way of affiliate links — you are welcome to post your own, but if you don't include one, the system will automatically add Kinja's — or possibly, advertising or ads benefiting the blog publisher will only be available to those with a licensing agreement. Right now we're still in the early stages, so there's a good chance that nobody knows.