I don't know what sites you're trying to use flash on, but the flash people stopped issuing updates for Android I think I heard. So, Nook's flash player is going to get more and more out of date, and BN can't or won't be able to do much about it.
Many folks find that if the browser is in "mobile mode" they get that message, and if it is in "desktop mode," they do not.
Websites present different versions of themselves to you if they know you're on a mobile device.
Another indication that you are in the wrong mode comes from not being able to zoom, even with the hovering zoom buttons, in websites.
You can put your browser back into "desktop mode" from the settings menu, and I bet that will resolve this for you.