Trying to install Flash, message to close Chrome even though it's closed

If you're using any Chrome apps like Hangouts, they keep Chrome running in the background all the time.  You'll need to exit those, too.

It's possible Chrome, or some other application identifying itself as Chrome is still running in the background.  Use Task Manager (Windows) or Activity Manager (macOS) to see what 'Chrome' program is still running and then terminate it.

Note, however, that Google embeds Flash Player in Chrome and there is no need to install it separately.  Chrome does disable Flash by default and you most likely just need to enable it.  See Use or fix Flash audio & video - Computer - Google Chrome Help  troubleshooting steps.