After reading the instructions you posted, it seems fairly simple via floppy for method #4:
Method 4. Boot to DOS and run
When running the flash program, you
must specify the /f switch:
flash /f prom0008.img
(note: with some older code sets the
'/f' switch is not required e.g. just
If you want to make a DOS boot floppy, all you need are three files: IO.SYS, COMMAND.COM and I think CONFIG.SYS (can't recall accurately) but the easiest way to make DOS boot floppy is to go to www.bootdisk.com. Download the boot disk maker and follow instructions on making that bootable floppy.
On that same floppy, copy the flash.exe and the new ROM image (in the example's case prom0008.img). Boot the system off of the floppy. Once you get to a command prompt (C:>), go to the floppy drive (presumably A:), and run the flash program as the example showed (A:>flash.exe /f prom0008.img).