Out of all the Facebook, King.com, & other social/casual web games I've seen my family play, 100% of them have been Flash. I think in years past some have been Java, but I've not yet seen a HTML5 game in use on the big sites as played here.

Since my family doesn't pay money into these games, their style involves playing broad coverage of games: They play each for a little bit until the life meter runs out, and often try new games. Again, 100% have been flash.

There are also tools & frameworks like Starling for converting either AS3 code, Flash assets, or full SWF files to other non-Flash platforms. For instance, I wrote the sorting algorithm in as3isolib, and noticed that Ubisoft ported one of their games using it to iOS, using Starling.

Flash is certainly alive and well.