If you *have* to run flash content (more than just Flash video) then your options are pretty much limited to a Windows tablet. iOS doesn't support flash, and Android supports it if you install the Flash APK via an outside source - and even then, the only browser that really supports Flash content is Dolphin HD. Most sites that play video have implemented HTML5 players - Flash games won't really work well at all on any touch-based device since they depend on mouse hovering and such for the most part.
Anyway... depends mainly on your budget.
Android:
You can get a Nexus 7 (7"), or Nexus 10 (10") - or the Nexus 9 that just released (9" tablet).
Windows:
There's the Surface tablets, but can be kinda spendy. A nice budget one is the HP Stream 7
Apple:
iPad / iPad mini