Flash Player is actually a built-in component of Chrome (and Chrome on ChromeOS). The bits are distributed directly by Google, so there's nothing for you to install.
What *is* probably happening, is that you need to activate Flash Player. Chrome blocks Flash by default. The site doesn't see it, so assumes it's not installed. If you click the lock icon in the address bar and choose Adobe Flash Player > Allow, you should be good to go. It's also worth complaining to the elearning vendor, as Flash Player support will be removed in Chrome soon. If they don't have a migration plan that moves them away from Flash in the near-term, you're going to have huge technology headaches.