Flashrom is your only option (apparently Dell has their own tool for supported Linux models). On desktops, you should be pretty good except for the latest Intel boards. Make sure your version of flashrom is current- it's not too hard to compile by itself, and a lot has changed since older versions.
Check with flashrom -V first. If it finds a flashchip, you're probably in good shape (even better if no operation for your chip is listed as untested).
If flashrom does find a chip, make sure you make a backup of your existing BIOS using flashrom -r original.bios.
If this backup works fine (make sure to look inside the file to make sure it's not all 0's or FF's), you can then try writing the new BIOS. I would highly suggest using flashrom -Vw to make sure you (and anyone else) knows exactly what happened.
Hopefully everything went well- if not, whatever you do, DON'T REBOOT OR POWEROFF. The folks on the #flashrom channel and the mailing list are amazing, and will help you.