You want to flash a Dell bios but do not have Windows installed. The official Dell support site does only provide Windows executables. An additional constraint is that your computer does not have a floppy drive or you ran out of (working!) floppy disks.
Fortunately, Dell provides a program package called biosdisk which builds a FreeDOS based boot floppy image. Using your default boot loader such as grub, you are able to boot this image from your hard disk so that you don't need additional peripherials.
./biosdisk mkimage <exe filename>
title Dell Bios Update kernel /usr/lib/syslinux/memdisk floppy initrd /DME521-010104.img
Usually, the flashing should start immediately but I had a small problem to defeat: DOS does only handle filenames up to a length of 8 characters (8+3, remember?) and so does FreeDOS. The biosdisk script does not handle this situation so you will get a "command not found" as last output. This is no problem, just start the flasher program manually by typing "DME521~1.exe" (or the the name of your executable). Maybe it is a bit tricky to find the "~" character because FreeDOS uses a US keyboard layout by default. Using a QWERTZ keyboard, I found it finally pressing the "" key.
Grub can't read files from LVM and Fedora/CentOS use this as default for the root file system. If you did not change this when installing your Fedora, you should move the memdisk binary to /boot and modify the grub configuration so that is says 'kernel /memdisk floppy' (paths in grub.conf are relative to /boot)