Purposely engaging in racially-offensive speech for the purpose of complaining about the subsequent accusations of racism.
The word was coined by a commenter after Matthew Yglesias, an author and major political blogger, bemoaned the lack of a suitable term for the behavior on his blog.
It plays off of the sports-related definition of flop. In both cases the flopper is trying to make the other person's behavior appear to be the problem. For the race flopper the "foul" is usually being too PC.
Shock jocks are often accused of race flopping.