Can you tell us what isn't working? I'm guessing that your browser says cookies are enabled and some website says otherwise, but that's only a guess, and if we knew wat the problem was (and perhaps which website) we'd be in a better position to answer.
In the meanwhile, you could try using a different browser, in case the problem is some other feature of the website which doesn't work properly. And if the problem is to do with flash that's common to pretty much all Android (and iOS) browsers: Dolphin can work with flash, though I don't recall whether root is needed as well, but very few others.