you cant actually damage hardware by using beta bioses.
in order to do this you need to create a bootable floppy disk. this is done by formatting a floppy disk and selecting copy system files.
then, you unzip your flash program and older bios and copy those onto the disk, then boot using the disk and you should be able to flash your bios no problems.
i found that its better to flash in dos mode when i upgraded my bios, i never had problems with the windows utility when i was using it but downgrading the bios can be a problem with windows based utilities
*edit* there's another version of the program that will only work in dos. you need to download that. the one you showed in your screenshot is for windows only