See the docs to give needed info:
https://kaosx.us/docs/
In Live mode when the install fails you will have a ~/installation.log
Also show the disk setup before you start the install:
sudo blkid
sudo fdisk -l
What options have you tried? Manual? Automated? Using only root for all? Or is this an UEFI setup where the EFI /boot partition is needed? Or tried with using different partitions for root, var, home, boot? Are you starting with a GPT or ms-dos partition-table?
You mention using USB stick for the media, how did you create? dd? imagewriter?