I haven't seen any information on this process, so I figured that I should write one just in case it could help someone.
With the Custom Deployments on the SDA released in version 6, I figured out a way to deploy out BIOS updates to Dell computers. This is super helpful if PXE is the first boot priority, so you can set a boot action and PCs will update upon startup.
So the first thing to do is to get the Dell BIOS update file for your model PC. I've so far tested this with a few Optiplex and Latitude models. Assuming that your KBE is x64, you will need the Dell 64 bit BIOS install utility here:
You will want to put both of these files in a zip folder, and go to your SDA.
On the SDA, create a new Pre-Install task, upload the zip file, and set the command line to "Flash64W.exe /b=$bios_file_name /s /f /r". Save this.
Then go to the Custom Deployments, create a new deployment, and add this task to the pre-install tasks.
After this, save it and you are done! Just boot the computer to the KBE, choose "Custom Deployments" and select the BIOS update for the specific model, and start the deployment. You do not have to check the box to restart automatically. The BIOS update command will automatically restart your PC.
I set all PCs to use PXE as the first boot option in my organization. This helps me when I create a boot action for a specific set of computers, so they will automatically run that boot action. If this is the case in your organization, create a boot action with your new Custom Deployment, and those PCs will boot to that action, run the BIOS update, then restart to update the BIOS, then boot back into Windows.
If you have BitLocker enabled, you will need to suspend that before running a BIOS update.