I'm trying to download flash player 9 in my computer. I keep getting a message to close Chrome to finish downloading. Problem is as far as I know Chrome is closed when trying to finish. My computer shows it is closed.
It's possible some other process is identifying itself as Chrome, you would need to open Task Manager and view processes for all users.
With that said, Flash Player 9 is very old and insecure. It's missing tons of security fixes. Additionally, since Google embeds Flash Player in Chrome, Chrome will not load previous versions of Flash Player. Only current version (or newer beta versions).
Chrome Apps like Google Hangouts will keep the Chrome process running even after you've exited the browser itself. You'll need to exit those as well.