The file you've downloaded for Flexi content is just a plain component installer. It does not need to be extracted prior to install.
So go ahead and go to your joomla sites administrative backend. Login, and from extensions choose install/uninstall.
From upload package file, choose browse, find the flexi content package, and choose upload file and install.
If your installation was successful, you should see "installed successfully" in each one of these fields.
Next, to access flexicontent go to components, and then flexi content.
Right off you might notice this notification here. In order to get things up and running with flexi content, typically you can enable all of the settings on the right.
So, publish all plugins, install default type, install default fields, and set php thumb cache permissions.
To get your sites current sections, categories, and articles working with flexi content, choose import joomla structure. It gives you this notice, but just choose Import Joomla Data.
Select close and refresh dashboard, and now all of your joomla data should be accessible from within flexi content.