It's not that hard to install Kali on your Android device and if you have enough space on your phone, you're good to go.
First of all, download Linux Deploy app. This app lets you to easily install any Linux OS that's supported for your phone.
Open it, setup the distribution (Kali) and setup your screen VNC width and height to resolution of your phone (e.g 1920x1080 if you have Nexus 5, Htc One and other FullHD phones).
After setting, click on install. Make sure you have enough space on your phone (about 7GB is required). After isntalling, click on reconfigure. After reconfiguring, click the START button and mount the system.
Download Android VNC Viewer.
Setup it like this:
Color format set to 24-bit
Open terminal, type sudo apt-get install software-center to install Linux software center.
Now you're running Kali!
To stop it, just go back to your Linux Deploy app and stop the service. That's pretty much all.