Adobe is no longer updating mobile versions of Flash. JellyBean, the latest Android OS is not compatible with Flash. Searching suggests that there are ways to access Flash on Android, but it requires some effort. Google has taken Flash out of the Google Play store as it is no longer supported. Ipads don't support Flash either.
http://www.theverge.com/2012/8/14/32...r-android-dies
All that said and done, I'd suggest the Nexus, since you'll be able to get all the latest updates directly from Google. I think both Kindle Fire and Samsung have fiddly bits added by the manufacturer and you'd need to wait for them to do updates, which means you could be stuck without the lastest features.