I also assume you are talking about the club scene where he dances with two girls.

Lindyhop is a good guess but there actually isn't any official Lindy in there. It's a good smattering of various swing and jazz dances. Specifically, there is 6-ct. single step east coast swing, a small amount of lindy-charleston, a bit of 20's charleston, some basic aerials, and a few classic jazz moves (peckin' and truckin' specifically) that you'd see in a dance like the Big Apple (circa 1937, attributed to Frankie Manning).

Wikipedia has a decent article on the jazz era of dance: http://en.wikipedia.org/wiki/Swing_%28dance%29 (search "Swing (dance)" if the link doesn't work)

You can also do a search for Frankie Manning if you're interested in that era of dance.

A few books to check out are: "Frankie Manning: Ambassador of Lindy Hop" by Frankie Manning and Cynthia Millman and "Jazz Dance: The Story of American Vernacular Dance" by Marshall & Jean Stearns. Frankie's book is phenomenal to ready and feel as if you are actually there experiencing everything he is relating and an amazing piece of history. Stearns book is more of a reference book but has a phenomenal amount of information in it.

Hope that helps!