Adobe has stopped supporting the Flash Player Plugin for Android back in September 2013. The last version was 11.1.115.81 for Android 4.0. https://helpx.adobe.com/flash-player/kb/archived-flash-player-versions.html

Some websites currently need a much newer version of Flash Player. For video HTML5 is getting more and more used as time goes on.

Actually you may not be able to install the old Flash Player for Android on this tablet.

The Asus ZenPad S 8.0 Z580C has a Intel Atom cpu (either a Z3530 or Z3580 which are also 64-bit) and not a ARMv7 type of cpu that the old Android 11.1 Flash Player needs.

James, it seems like you may be right. I found the instructions for installing the last version of the Adobe flash player from the Adobe archives. I followed the instructions and seemingly installed the player, at least it appears in my "apps" on my tablet, but it still won't play Flash video, I can't even see the Adobe setup /test page when I tap on the gray "plug-in" box. I have the tablet with the Z3580 processor.

I guess I'm stuck with having to install whatever app is offered for the site(s) I'm trying to view or installing yet another browser that offers Flash support. (I already have 2 browsers: Chrome, which was installed by Asus, and Firefox, my browser of choice.)