You can boot from the DiskWarrior flash drive but it is much faster to boot from a copy on your Harddirve or SSD.
I have it installed in my applications folder so it gets Cloned along with everything else when I make a cloned backup.
Diskwarrior cannot act upon the drive it is running from, so I boot from the cloned backup and then run DW on my main boot drive to effect repairs if any needed.