But that is very much beside this article's point, which is kind of surprising - it's a very clearly written article.
Web designers mostly should not be doing the things that Flash/HTML5+Canvas make possible. Gratuitous animation and sound, non-standard UI, and the breaking of web fundamentals are not strictly Flash problems, but poor design practices that Flash does (and which HTML5+Canvas probably will eventually) seem to encourage.
Nielsen's point isn't that Flash is bad, per se. The problem is: unless you're producing a piece of pure entertainment (games, Homestar Runner, etc) then deciding to use (or emulate) Flash is, statistically speaking, almost certainly a design mistake. A big one.