Amazon Prime on Nexus 10: Works for Me
After a bit of trial and error, I was able to install the Adobe Flash Player and Firefox browser. Having done that, I now have the ability to view Amazon Prime TV and videos on my Nexus 10!! Moreover, I did not have to root my tablet (a big plus since the last time I programmed was back in 1976 or so).
Although I didn't take notes, here's basically what I did:
-TEMPORARILY enable the Security setting that allows one to download apps from sources other than the Google Play Store.
-Google around and find a thread that has a link to the Adobe Flash Player 11.1 download. (There are several of them...you can find them by trial and error using terms such as "download flash player 11.1 apk"; "how to make flash player work on Nexus 10"; "android jelly bean flash player download", etc. Note that you do not want the most current Flash Player; it needs to be an earlier version such as 11.1.)
-Download the flash player apk file to your tablet. It should install itself automatically but it it doesn't, you can use the ES File Manager or equivalent to find the file and click on it, to do a manual install.
-Once you have the Flash Player installed, be sure to reset the Security setting back so that unknown apps can NOT be downloaded to your tablet. This is important; don't forget to do it.
-Go to the Google Play Store and download the FireFox browser app.
-After you do that, open FIrefox and make sure it works OK. Then reboot your tablet so Firefox and the Flash Player can synch up (this may not be absolutely necessary but I did it just in case). When you reboot the tablet and start FireFox, you should then be able to log into your Amazon Prime account and access TV and movies.
-When viewing a Prime video via Firefox and Flash, the default volume setting will probably be too low, even with your tablet volume control turned all the way up. However, if you tap on the bottom of the video screen, a menu bar with the "Pause" symbol will appear. There is a volume control over towards the right side of the bar. If you slide the volume button (circle) over, the volume will increase.
I apologize that I am not able to give a crisp, concise description of the exact steps I took but the above is pretty much what I did. Hopefully it will be of benefit to someone else out there who has an Amazon Prime membership they want to take advantage of, using their Nexus tablet.
By the way...from what I read online, Dolphin, Boat and other browsers also supposedly work with Flash. However, I was successful with Firefox so I figured I'd quit while I was ahead. I believe Firefox is also mentioned on the Amazon Prime site "Help" as a supported browser; that was another reason I chose it.
Good luck and let me know how this works for you. If I've misstated something please post a correction so others can benefit from your experiences as well.