Hi all,
My first post. I ended up here also because I couldn't get flash videos to run on my Galaxy Note 10.1 (2014). A simple Google search shows this is an issue with lots of thoughts and suggestions, but if you've come this far in the thread, you are still looking. FWIW, I followed dianehelen's list above to a "T" and then added in one more step and (for the moment, at least), I have full flash features in both Firefox and Chrome! I'll list my steps below -- and a big thanks to dianehelen for her help in getting me 90 percent of the way.
Background: Android no longer supports Flash, so when you go to a site that requires it, you're kinda screwed. But there's a workaround (caveat: it worked for me, and I hope it will work for you, but I'm only a newbie, so...)
Step one: you'll need an archived version of Adobe Flash. Do a search for "archived flash player" or go to this link:
Archived Flash Player versions Scroll down the page until you find the "Flash Player for Android 4.0 archives." I chose version 11.1.115.81. Don't forget to go to settings-->general-->security-->device administration, and check to allow "all installation of apps from unknown sources." Otherwise, the tablet will not allow you to download the apk. Next, download a copy and install it (I used MY Folder, following dianehelen's (dh) instructions).
I can't speak to setting up Chrome to work because I only "set up" Firefox, and thereafter Chrome just seemed to work. So for Firefox, I uninstalled my previous copy and then reinstalled a new one. I then downloaded the “flash video downloader” addon for Firefox. I also enabled plugins (under FF settings; the addon list is under “tools” in FF). Finally, also under FF settings, I chose the “request desktop site” option. And voila, I have flash videos running just fine.
I'm always grateful when I find something that will get me where I want to go (in this case flashville), and so I hope this will help someone else. I've had this tablet (my first) for 4 days now and there IS a learning curve. Next up -- trying to find a decent case/protector and keyboard.