Linux Shout published a tutorial about installing and use Kali Linux on Android without root.

Install and use Kali Linux on Android without root

Steps to install Kali Linux on Android smartphone without rooting to run command-line hacking and penetration security testing tools. We generally use the Linux operating system on Desktop or Laptop because on Android it is not stable to use GUI-based Linux OS, however, the command line will be. Yes, we can set up Kali on Android, which is popular and known for its security testing tools. So, let’s start with the tutorial, and yes you don’t need to do any modification in your Android OS that would temper the warranty of your phone.

Install and use Kali Linux on Android without root - Linux Shout