I have a Gigabyte motherboard. To update (flash) BIOS requires no operating system:
1-download new BIOS container from Gigabyte web site
2-extract BIOS from container onto FAT formatted USB stick
3-place USB stick into motherboard USB socket
4-boot into BIOS setup
6-select stick device
7-select file to flash
Just “tested” procedure by updating from B250MD3H.F9d to B250MD3H.F10. IME, most newer motherboards provide a similar procedure.
More than likely if the new firmware and installer supports only MSWindows, it’s in the form of a CAB file (inspect the downloaded file).
There are various utilities that can extract a CAB file, I understand WinZip(if you have a MSWindows machine available) supports nowadays, a quick search returns “cabextract” which runs on Linux.
After the file is extracted, take a look at what you have, often can be executed in Linux (assumes is script or C code).
Don’t overlook possible Linux support for firmware, drivers and software from the manufacturer.
This poorly communicates whether you have been helped or need more help. We need more information if you still need help. What is the model of your Gigabyte motherboard? Have you download a BIOS update file? If yes, what type of file is it? The file command will tell you. If it is a .EXE file it might be a .ZIP file in disguise, extractable with any number of common unarchivers. If the motherboard’s support page does not provide instruction for update directly from FAT formatted device, you may nevertheless be able to install an extracted BIOS via the flashrom utility provided as an openSUSE rpm.
Mainboards which do not support BIOS/UEFI flashing via the BIOS interface itself – independent of whatever operating system is installed on the box – are absolutely not suitable for anything which isn’t a dual-boot system …