Flashing an HP 2140 with free software

When I flashed the Mini 2140 yesterday I used a Windows laptop to create a bootable flash drive with the BIOS utility and update on it.

I didn't really need to use a non-free operating system, as HP provide a tiny bootable ISO image with FreeDOS, but using that means wasting a CD-R. It's not that those are expensive, but they do end up in landfill.

Instead, I'd like to be able to simply use a USB key. I found some help on the FreeDOS wiki and I thought I'd document the steps I followed on Ubuntu.