I've written up a detailed guide
on my blog describing how I rooted my Verizon Samsung Galaxy Note 3 on my MacBook, but here is a summary:
1. Install VirtualBox
2. Install VirtualBox Extension Pack (on VirtualBox download page)
3. Install a Windows XP virtual machine
4. Enable USB 2.0 in VirtualBox for the Windows VM
5. Install Kingo inside Windows
I'd love feedback as to whether this works on Linux as well.