How do I create a bootable flash drive running MS-DOS 6.22?

Around the time when Windows 98 was mainstream, bootable MS-DOS CDs and USB drives used a 1.44MB floppy disk image as the actual boot target. The CD/USB drive stores the floppy image either visibly on the file system or invisibly outside of a partition, and the computer would boot to a virtual A:\ drive. If access to the CD/USB drive is desired after boot, the appropriate driver must be present on the floppy image and loaded.

At least in some cases, booting from the floppy image requires features implemented in BIOS. (I remember trying to make a rescue disk on a state-of-the-art 32MB USB drive, and there being different instructions for BIOS that support USB-FDD, USB-ZIP, USB-HDD, etc.)

If you don't feel like hunting down period-appropriate documentation and tools, your best bet is probably a MS-DOS floppy image paired with a modern bootloader that supports memdisk features. syslinux/isolinux and GRUB4DOS comes to mind.

Rufus author here.

As explained here, Rufus does not embed any version of MS-DOS with the application, so it doesn't matter what version of Rufus you use, you won't magically get a specific version but the Windows Millennium DOS version that Windows provides (that is, up to Windows 8.1, since Windows 10 removed it altogether, so there's no MS-DOS creation option in Rufus if running on Windows 10 or later).

Now, your expectation is that Rufus can create an MS-DOS bootable USB if you provide your own version (as an ISO, or something else). This is not the case. Rufus cannot be used to create an MS-DOS bootable USB drive except a Windows Millennium one, if you are running Windows 8.1 or earlier, and, because the demand for such a feature is exceedingly small (at this stage, I have to point out that the amount of people who have been able to claim that they have found a genuine flaw in FreeDOS that forces them to use MS-DOS currently stands at exactly zero, as most of the "issues" that people have with FreeDOS only have to do with a slightly different way to handle AUTOEXEC.BAT/CONFIG.SYS or menus, which is easily addressed and does not constitute a DOS incompatibility), I have no plans whatsoever to ever add that functionality as I have 100% confidence that FreeDOS can always be used in lieu of MS-DOS.

The only way I would ever consider adding this feature is if the following conditions are met:

• You can demonstrate that you have found an actual incompatibility between FreeDOS and MS-DOS (rather than a "belief" that there may exist one, which, in years of being subscribed to the FreeDOS mailing list I have yet to see).
• The FreeDOS developers indicate that they are unwilling to address this incompatibility.

Short of these two conditions being met, I will respectfully request that you either use FreeDOS (which, again, I have yet to see fail compared to MS-DOS in terms of compatibility) or another utility than Rufus.