Recap: Flash was running fine on my Nexus 7 with JellyBean. Once I upgraded to KitKat, all bets were off. Now with KitKat 4.4.2, Flash lives again, in the Dolphin Browser.
It's all explained here:
http://www.phonearena.com/news/Here-...KitKat_id49851
The upshot is you need to uninstall the Flash player, then install the Dolphin Browser with JetPack. Reinstall Flash Player and you are good to go. I can now stream Amazon downloads like I did before - fast and no lag.
Good luck!