I suspect that you've gotten your web browser into "mobile mode" by accident (or that you're using Puffin, which does not support flash in the free version that the BN store has.)
Many websites offer two versions of the site depending on if your browser is telling them you're on a desktop or on a mobile.
The desktop version usually supports flash in the Nook browser, and the mobile version often does not.
The desktop versus mobile preference is one of the ones controlled by the settings menu that also controls plugin loading, default zoom, etc.
Flash is not something that's easily upgradeable without either waiting for BN to push an update or rooting your device, uninstalling what BN put on it and downloading the Android market version, but even that won't fix 95% of the "you need to update your flash" errors on websites.
Thanks. I had posted a similar question awhile back. This is something to check out.
I think the current Flash is 11. It's available on the Android Market...but not for NT unless you're rooted, etc....