I’m quite surprised that flashrom works pretty much out of the box on FreeBSD running on my Alix 1.C board. All I needed to do was comment out the code in the enable_flash_cs5536() function part of the chipset_enable.c file. Then, this simple command let me read out the BIOS image:
$ flashrom -f -r -c "SST49LF040" bios.bin