Any SPI flash programmer should work though. The protocol is simple enough that you could even implement it with an arduino if you really needed too.
Not sure what they used here, but I've had good success using a FlashcatUSB on various embedded devices and it has support for a pretty broad variety of flash memory chips.
Not sure what they used, but even a Raspberry Pi + a Pomona clip will do the trick. Have a look at the flashrom wiki, see https://flashrom.org/ISP.
Careful though, and read the datasheet first! AM4, for example, uses 1.8V SPI flash chips. Connecting them to Raspberry Pi directly will at the very least fry the chip, if not the whole board.