It's the same bios, regardless of operating system. The problem would be trying to run an xp program in vista to do a bios flash within windows. However, you don't want to ever flash a bios using a windows utility. Bios flash + windows = bad.
Most bad flashes and bricked motherboards seem to be as a result of flashing from within windows.
Can you update an emachines bios with a floppy or usb stick?
And the single most important thing. Why? Never flash your bios unless you need a more recent version so that you can install a cpu that needs the newer version to support, or you are experiencing an issue that is fixed by the new bios. There is no reason to flash a bios that doesn't need it, and just for the sake of updating, is not a valid reason.
If it ain't broke, don't fix it. Does the motherboard currently work? If not, what is the problem?