[ikk157]

Unfortunately, I couldn't find any method for this. All tutorials I have found so far are about running it on Raspbian Pi's with a  SD card and USB drive. Even that need a USB drive with at least 16GB space. Looks like most of those small distros need an 8GB or bigger USB.

I did some of my own research and came to the same dead end as you did.

However, I thought of something that COULD work.

Download the raspbian desktop image (not the raspberry pi version, the pc version). Flash it into another usb flash drive (not the one you want to install it on) like you would to let’s say, create a bootable windows installation drive. Boot from it, then plug in the usb flash drive you want to install raspbian on. When you come to the prompt where it asks where you want to install it, see if the usb flash drive appears, and choose it instead of choosing your hard drive. The rest should be self-explanatory. You might have to try formatting the usb flash drive to different filesystems and see which one is detected by the installation.

Yet again, this COULD work. I have never tried it. For a matter of fact, I just came up with it. If you decide to give it a try, please update me on the outcome.

Good luck!