Does it have an operating system?
I don't know.
Well, it needs one in order to install Flash Player.
Most smart TVs have Chrome OS, which has its own Flash Player built by Adobe, but modified by Google. Nothing can be done with it here.
See: https://groups.google.com/forum/#!topic/alt.tv.tech.hdtv/Sy5SA4mWcX8 for info on how to update it.
An old thread I know.
My guess is you want to watch video content in the browser, I tried there is no way to do it if it requires flash.
The best workaround I found if there was no app available on the TV was to use "screen mirroring"
It works for me with Epix.
I just screen mirror my phone, play the video on my phone and screen mirror it on the TV.