In all likelihood, rebooting the computer will probably solve this. We don't force you to close Chrome to uninstall because it's inconvenient, but the consequence of that choice is that Chrome might still think Flash is installed. Rebooting should eliminate any possibility that something running is simply confused.
What's weird here is that Chrome ships its own copy of Flash Player, and our uninstaller doesn't delete it (a future Chrome update will drop support for Flash Player and remove its encapsulated copy). I'm happy to help dig into this more (uninstalling and reinstalling Chrome is a decent brute-force approach to fixing it, but I'm curious about what's actually happening), but I bet that the reboot solves it.