Folks, this thread could go on for ever... "I love flat!" "No, I hate flats!". So let's just agree that it's just a different flavor and that Flats and Rounds both have their place in our world.
To answer the OP's question, I previously read the industry has indeed observed an increase of bass players using flats, however a large majority of players is still using rounds. Between you and me it's a good thing for string makers as one don't change flatwound strings as often as roundwounds.
5 years ago I started to notice more and more pros when talking about their gear in Bass Player, mentioned using flats, most of them being young and hip players such as Justin Medal Johnsen and many young players from Alt Rock or Dub/Reggae scene. I remember going to Guitar Center and buying a set of D'Addario Chromes. I told the GC guy. "I have a feeling you are going to sell more of those". In return the guy looked at me like if I was a total idiot. But we all know how savvy those GC guys are...
Personally I like and use both depending on the type of bass. P Bass Flats, Yamaha TRB1005 rounds, Stingray Rounds...