Windows 8.1 64 bit
Chrome Version 41.0.2272.76 m
Flash Player is a built-in component of Internet Explorer. There's nothing separate to download or install.
PowerPoint is basically just using an embedded IE window to play the Flash content, so if Flash Player isn't working in IE (you probably *did* damage the installation by trying to delete it), then it's not going to work in PowerPoint either. Since there's nothing to download or install on Windows 8 for either Flash or Internet Explorer, solving this gets weird.
What you need to do is look in Add/Remove Programs (I forget exactly what Win8 calls it) and choose the Windows Updates list from the left-hand column. You then need to look for the most recent update to Internet Explorer. Remove it, then run Windows Update again to pick it back up. This will usually straighten things out.
Thanks, Jerome. I think installing the latest Articulate Studio version somehow fixed the problem, because I don't get that message anymore. But if it comes back, I will do what you suggest. Thanks for your time, I really appreciate it.