Are you seeing that same Bios update available in Win 10 under Optional Updates?

If you are, you might try that.  I have had two other machines where the downloaded version did not work but the Win 10 one did.

The attempted install may also create a log.  If you can find that it may give a clue as to what is happening.

I would suggest you try doing it manually from a usb flash drive disabling bitlocker if enabled before flashing.

Installation
Note: You must provide a bootable USB drive. This executable file does not create the DOS system files.
1. Copy the downloaded file to a bootable USB drive.
2. Power on the system and then Press the F12 key.
3. Select USB Storage Device and boot to the DOS prompt.
4. Run the file by typing following command. For example:
C:\ XPS_9360_X.Y.Z.exe
Where C is the drive letter of the USB device where the executable file is located and XPS_9360_X.Y.Z.exe is the name of the downloaded file.
The system restarts automatically and updates the BIOS at the system startup screen. After the BIOS update is complete, system restarts again.

There is no "Optional Updates", I see "Other formats" and it has a recovery image file. (.rcv)

I can't find any log files. 

Hi bacillus1!

It didn't work...