leaving one cookies

It seems that if you use sites that go through Cloudflare that flash cookie wil get reinstalled. Is that what's happening, you think?

Anything helpful at these sites?

http://www.aboutcookies.org/

has a link to the flash player control panel, this links you directly to the control panel for your computer:

http://www.macromedia.com/support/documentation/en/flashplayer/help/settings_manager07.html

and to the firefox addon "BetterPrivacy 1.68", never used it, though.

https://addons.mozilla.org/en-US/firefox/addon/betterprivacy/

Although you didn't state you use Internet Explorer I wonder if the cookie could be from it, if so perhaps give Nirsoft IECookiesView a try to see if it finds it associated with IE. There's also a version available for Firefox called MozillaCookiesView.

Can't forget cookies can be written into the Windows registry.

It's a flash cookie, but Andavari is correct it maybe in a different flash cache than your usual Firefox. Try the flashcookiesview from the same site as he mentioned as well

http://www.nirsoft.net/utils/flash_cookies_view.html

And also make sure firefox doesn't have any add-on that you don't want esp one from said internet site. Also open internet explorer's flash control panel or settings whichever they use and delete all cache, history ect for that flash

To follow-up on Andavari's registry suggestion. Open regedit with administrator privileges and search the site's name (without .com will give your more hits). Assassinate each and every found instance (within reason)