The gimmick, for those who are unfamiliar: somebody makes a post declaring a kink meme, and people post in comments (frequently anonymously, occasionally not) with requests in the form of fic prompts. Others than comment on, typically in the form of enthusiastic seconding, or write fic in (frequently anonymously, occasionally not) in reply to these requests as they are made. These requests typically embody some specific kink, hence the meme. From what I gather, the idea's antecedent is probably the anonymous love memes that go about every so often, where people post their username and others then anonymously make nice comments about them. But I don't know where or when people started writing fic in these things. (Fanlore has no entry for the concept of "kink meme," which seems to me to be a pretty gaping hole given that several fannish pages refer to kink memes.) The first one I remember seeing was for the 2009 STAR TREK flick, but being as I am not in fandom for the porn and because there are huge areas of fandom I know absolutely nothing about (see: SGA), I don't know when it started or in what fandom.
The other curious thing about the kink meme, to me, is that the anonymity function is designed to facilitate people asking for/writing exactly the kinky perverted fanfic they're asking for with no inhibitions from some attendant sense of shame. This strikes me as odd, because as several fandoms -- most especially SUPERNATURAL -- have made it abundantly clear at this point, fandom *has* no sense of shame.
("Damn, they're hot! What? They're brothers? OKAY INCEST IS AWESOME NOW YAYE.")