The problem with Flash -- as I remember it -- wasn't the animation so much as how the Flash embed 1) required a plugin, 2) didn't interact as one would expect of a web page (e.g. right click), 3) was slow to load, 4) and didn't play nicely with the surrounding DOM.

I don't think this is the case here. For a CTA button (literally "Call to Action"), I think it's perfectly acceptable to add an animation to it.

Everyone making so much a menace about the 90's coming back. Please let it happen man! it can't be too much worse than this!