Don't know when flopping got so easy to see at the NBA level but it sure does seems to coincide with the internationalization of the players. Most of those players were probably brought up playing and watching soccer.
As an aside, NBA flopping has become almost as comically entertaining as soccer flops. Of course, that's probably because soccer players can fly through the air and only have to worry about landing on soft turf and not a hard wood floor.
LeBron playing and watching soccer? 
Internationalization of the players. Meaning when players born outside of America started playing regularly here in the NBA.
Yeah I got that.
I guess LeBron just learned from their ways...?
Well once one player does it, everyone has to do it. Sort of like Michael Jordan's long shorts. 
This got me thinking, so I did some serious investigative work on my own.
Casually, you will see discussions of flopping attribute it to the Euros and soccer:
"The ugly trend of faking physical contact began in soccer...now the NBA will have an opportunity to deter players from trying to simulate violent contact in ways made famous by Vlade Divac, Manu Ginobili and Anderson Varejao."
http://sportsillustrated.cnn.com/2012/writers/ian_thomsen/09/28/nba-flopping-david-stern/But, a lot of the great floppers predate the Euro invasion. This earlier article points out that Reggie Miller, Laimbeer, Rodman, et al. were flopping at a high level even in the late 1980s.
http://sports.espn.go.com/espn/page2/story?page=neumann/070607You can quite clearly see Laimbeer, named in the previous article as the best of all time, executing a very convincing flop at 0:45 of this video:
http://www.youtube.com/watch?v=hMiVs2SInCYAnd even later in that video someone is holding a sign referring to Laimbeer as "flip-flop," indicating early use of the term.
[Aside: there is an absolutely classic clip of Johnny Most going wild - with no audio, which somehow makes it even better - starting at around 1:40.]
Vlade, who will spring to everyone's mind as the first great Euro flopper, really did not become known for flopping until the 1990s, and was in fact drafted in 1989 so he really could not have predated people like Laimbeer. But he certainly contributed to the refinement of flopping as an art form.
I'd say ultimately that flopping developed like a lot of other things in America - probably from many influences all coming together from different places.
