... was a lot easier than expected. Just not very well documented.

First of all, you need the appropriate utilities. Debian users can aptitude install libsmbios-bin

Next identify your system. It will look something like this

$ sudo modprobe dcdbas
$ sudo getSystemId
Libsmbios:    0.13.10
System ID:    0x01D8
Service Tag:  ...REMOVED...
Express Service Code: ...although my warrany is over...
Product Name: MXC061
BIOS Version: A10
Vendor:       Dell Inc.
Is Dell:      1

The information you need is the "System ID".

Now you need to get the so-called HDR file for your bios. This can either be extracted from their EXE file using wine (with -dump-hdr or so), or you can find it on the linux.dell.com server. This page contains a huge list, and there are tons of dirs like system_bios_ven_0x1028_dev_0x01d8_version_a10. 0x1028 apparently is "Dell". The second hex number is your System ID. The last number (A10 here) is the BIOS revision. Pick the appropriate directory. There should be a bios.hdr file in there.

You can verify if the file is appropriate for your system:

$ sudo dellBiosUpdate -f bios.hdr -t

$ sudo modprobe dell_rbu
$ sudo dellBiosUpdate -f bios.hdr -u

When rebooting the next time, your screen might be garbled for a few seconds. At least it was for me. I was scared I might have trashed my system, but then it rebooted and had the new BIOS. So just give it some time (Fortunately I've done enough BIOS updates to know to just wait. I've even done a 'blind' video BIOS update on a Nvidia TNT. The first update had trashed the card, but I was able to redo the flash process without seeing anything on the screen, and guess what, the card worked again!)

In case you're wondering how this works: as I understand it, the dell_rbu driver will reserve memory for the BIOS update. Being a kernel module, it can just lock the memory in place until the next reboot. It will store that address in CMOS for the Bios and set the update flag. On reboot, the current Bios will check if that the stored image is still intact (I bet they do some checksumming here!) and then load that into the BIOS flash. That way, you don't need to boot into a low-level system such as Dos or Dos-Mode anymore to do an update.