I used VirtualBox version 5.1.6 to install Kali Linux 2016.2 x64 as a VM.
I made sure my system was up-to-date:
sudo apt-get update && sudo apt-get upgrade -y
I grabbed the VirtualBox Guest Additions:
sudo apt-get install -y virtualbox-guest-x11
Set up the following functionality:
Settings(Host + S) -> General -> Advanced:
Shared Clipboard: Bidirectional
Drag and Drop: Bidirectional
Then I rebooted the system;
Tried to drag and drop a directory from the Host to the Guest and nothing happened.