Is there a way to use Go Launcher icons in Folder Organizer? I really like Mitch S.'s Flat Icons. However, they are only available on Google Play packaged for Go Launcher.

On Windows, you used to be able to extract any icon in .ico format from icon library or an .exe file and use it elsewhere.

Is there an "app for that"&trade; on Android?

I'm specifically interested in using with Folder Organizer.
Android applications are distributed as 'apk' files. This is basically just a standard 'zip' file with a different file extension.
If you change the extension to' zip' you can simply extract the contents of any app.
In your particular case the icons will be inside the 'res' folder in one of the folders that have 'drawable'  in their names. 

They're standard 'png' files.