So, after reading the latest chapter, I think it's a reasonable guess that Kaido is a Mythological Zoan: Dragon (Japanese dragon). Take a look at this here. Kaido's got the same sort of beard, the same sort of tendril-y mustache, as well as the fact that he's got a dragon scale pattern tattooed on his left arm.
This all says to me that it's pretty possible that Kaido is a Japanese dragon Zoan. This explains why Momonosuke is such a big deal, because Momo would be an illegitimate form of Kaido's fruit.
More "proof":
1. It's said in this chapter that a person who attempts to fight Kaido would find themselves faced with "a Kaido". Quick Google search reveals that a "Kaidou" is a type of ancient Japanese road. Japanese dragons are known for being unbelievably long. Kaido as a dragon would probably be long enough that he basically would be "as long as a Kaido".
2. Dragons are known in their legends for being either one of two things: 1. Immortal. or 2. Mortal, but with incredibly hard, nearly-unpierceable skin that essentially makes them immortal unless you can find a chink in their armor. This pretty heavily draws parallels with Kaido, as well as gives him a potential weakness so he's not too OP.
3. How did the man manage to single-handedly get to a sky island in the first place? Yeah, he flew as a dragon.
4. This color spread (
http://bato.to/read/_/273060/one-piece-digital-colored-comics_v70_ch699_by_no-group/2) immediately after it's mentioned that the Strawhats are targeting Kaido. It's the Strawhats as a bunch of knights, "slaying" a dragon. Tell me that's not a serious case of foreshadowing.