The benefit of HTML5 is that it will work across all platforms. It's not a perfect solution for everything, but for something this simple, I imagine there wouldn't be any issues. You may sacrifice a couple of bells and whistles, but otherwise, I don't imagine too many issues. Flash will "never" work on iOS, so there's that. Android is very fragmented, in that there are a wide variety of versions, depending on the device your using. Currently, virtually every Android device should have the capability of running Flash, it's just a matter of doing a manual update at this point. Some older or cheaper devices may not run it smoothly, I imagine though. Android and iOS account for probably 90%+ market share, so there's no real need to cater to anything else. Blackberry is going the way of the dinosaur and Windows just can't get it's hooks in to the mobile space, despite throwing a bunch of money at it lately.
And here's a link to download flash for anyone that wishes to do so:Link