Yet another simple solution: Free DOS pre-built bootable USB flash drive image by Christian Taube. As of writing (2017-07-11), doesn't support versions of Free DOS more recent than 1.0 (current version is 1.2).
If your system is running UEFI (or you have a UEFI conversion Task Sequence), then it needs to boot the native architecture (in this case 64-bit).
(Dell offers this as a possibility on their site) Some notes before starting: If your flash image is too large for a floppy, go to the Free Dos bootdisk website, and download the 10Mb hard-disk image.
This image is a full disk image, including partitions, so adding your flash utility will be a little trickier: First find the first partition (at time of writing, the first partition starts at block 63; this means that the partitions starts at offset thus leaving more space for the flash utility and new BIOS image. Copy your BIOS flash utility and new BIOS image to the mounted floppy disk image.
Flashrom is a utility for identifying, reading, writing, verifying and erasing flash chips.
It is designed to flash BIOS/EFI/coreboot/firmware/option ROM images on mainboards, network/graphics/storage controller cards, and various programmer devices.