There are plenty of applications and extensions already created and available for music and video playback in Google Chrome. I have narrowed down the search for you to display only the applications you need.
Install apps and extensions: https://chrome.google.com/webstore/search/flv%20player
I have tested one and it worked quite well with its own interface. When you add a Chrome application, it will be added to the Chrome Launcher in your taskbar/systray.