These instructions apply to both atiflash and flashrom, command-line syntax is the same. When using flashrom replace "atiflash" by "flashrom".
Download the BIOS file (ATI BIOS collection here) and put it on a bootable floppy/usb stick/CD. Check www.bootdisk.com on how to get a boot disk.
The ATI BIOS collection has a new feature which serves you a bootable floppy image or bootable iso CD image with the BIOS you want on it. Click on "Advanced" when in the BIOS list.
Reboot your computer with the boot disk and run atiflash -s 0 oldbios.bin to save your old BIOS just in case you might need it at a later time.
Now run atiflash -p 0 newbios.bin Replace newbios.bin with the filename of the downloaded BIOS file.
If you are trying to flash a BIOS for a different card then you will get a security warning that the BIOS does not match your card. If you are absolutely sure that the BIOS is compatible you can use the -f parameter to force flashing. For example atiflash -f -p 0 BIOS.bin