I can only assure you, that the following steps worked for me. This "What worked for one user on a Dell Inspiron 1525 and Xubuntu, using Wine to extract BIOS image etc" on the mentioned wiki page is quite similar to my steps:
I've recently updated the BIOS of my Dell Latitude E6500 from version A27 to A29 under Linux Mint 17 KDE (= Ubuntu 14.04 LTS Trusty Tahr) with the CLI and here is what worked very well for me:
- Download the needed DELL Software
sudo apt-get install firmware-addon-dell smbios-utils wine
Check your BIOS version: sudo dmidecode -s bios-version
My output: A27
Download your BiosUpdateFile.exe (in my case E6500A29.exe) for your specific device from the DELL Support Page
Switch to the directory which nests your E6500A29.exe and extract the *.hdr file from it with the command: wine E6500A29.exe -writehdrfile
Update BIOS: sudo dellBiosUpdate -u -f E6500A29.hdr
Reboot: sudo reboot now
Check your BIOS version again: sudo dmidecode -s bios-version
My output: A29