I think what you're looking for is
flashrom. Provided that your system is supported, you can read your BIOS content by issuing
# flashrom -r <outputfile>
If you only want to save the so called CMOS RAM (those extra-bytes you save configuration to, like alarm on RTC et al) the kernel's
nvram driver and device might help you:
tristate "/dev/nvram support"
depends on ATARI || X86 || (ARM && RTC_DRV_CMOS) || GENERIC_NVRAM
If you say Y here and create a character special file /dev/nvram
with major number 10 and minor number 144 using mknod ("man mknod"),
you get read and write access to the extra bytes of non-volatile
memory in the real time clock (RTC), which is contained in every PC
and most Ataris. The actual number of bytes varies, depending on the
nvram in the system, but is usually 114 (128-14 for the RTC).
This memory is conventionally called "CMOS RAM" on PCs and "NVRAM"
on Ataris. /dev/nvram may be used to view settings there, or to
change them (with some utility). It could also be used to frequently
save a few bits of very important data that may not be lost over
power-off and for which writing to disk is too insecure. Note
however that most NVRAM space in a PC belongs to the BIOS and you
should NEVER idly tamper with it. See Ralf Brown's interrupt list
for a guide to the use of CMOS bytes by your BIOS.
On Atari machines, /dev/nvram is always configured and does not need
to be selected.
To compile this driver as a module, choose M here: the
module will be called nvram.