I would assemble the PC 1st. It's not that you can't flash it 1st, but anything can happen just when you don't want it to. Someone bumps the table and it restarts during a flash and your done. You probably wouldn't have any problems but why chance it.
I'll never flash my bios using a Windows-based utility. Quite a few members here have disagreed with me about this, but it's always a bad idea in my book.
Flashing with a Floppy Drive is a much more reliable option but I've seen Floppy Disks go bad just by looking at them.
I flash my bios using a usb memory stick/flash drive. To work with my system I had to make the Flash Drive Bootable which wasn't that hard but it was a pain in the arse.
However your mobo, the GA-X58A-UD3R, has a feature called Q-Flash which is really cool. Download the Bios update, I think F5 is the latest update and save it to a temporary location. The file is a .exe file that will extract the contents to a location of your choosing. Using the F5 bios as an example, go to the location of the bios files and copy X58AUD3R.F5 to a standard flash drive. Restart the PC, with the Flash Drive plugged in. When the System Posts hit the <End> key to enter the Q-Flash Utility. Or you can enter the Bios and then hit the <F8> key to access the Q-Flash Utility. Once your in the Q-Flash Utility you only have to Navigate to your Flash Drive and the location of X58AUD3R.F5, hit <Enter> and follow the on screen instructions.
The info about Q-Flash is in the Manual on page 72-73. Here's the .pdf link I used
You can also use Q-Flash with a Floppy in-lieu of the Flash Drive so you would only need 1 Floppy Disk.