Wiring of the BIOS chip
Pictures:

Wires soldered to MX25L6405D

Wires soldered to MX25L6405D, coloured

Sketch of the connection adapter

Notes:
The soldered contacts look all good and when the RPi is running, the MX25L6405D gets about 3.32V on the VCC pin.
Output on the RPi2 with Slackware ARM current
As root user:
# flashrom -p linux_spi:dev=/dev/spidev0.0 -c MX25L6405 -w x200_8mb_usqwerty_vesafb.rom flashrom v0.9.8-r1896 on Linux 3.18.9-v7-arm (armv7l) flashrom is free software, get the source code at http://www.flashrom.org Calibrating delay loop... OK. Found Macronix flash chip "MX25L6405" (8192 kB, SPI) on linux_spi. Reading old flash chip contents... done. Erasing and writing flash chip... Reading current flash chip contents... done. Looking for another erase function. Reading current flash chip contents... done. Looking for another erase function. Reading current flash chip contents... done. Looking for another erase function. Erase/write done. Verifying flash... VERIFIED.