Linux Hint published a tutorial about creating a Kali Linux Live USB Drive.

Creating a Kali Linux ‘Live’ USB Drive

This tutorial will show you how to install Kali Linux on a USB drive, add persistence so that you can save files on the drive and then run Kali from the USB drive. By the end of this session you will be able to create: a USB drive running Kali Live Linux, a partition for persistence on the USB drive, a file system on the new partition, and persistent files on the USB drive.

Creating a Kali Linux ‘Live’ USB Drive – Linux Hint