I think you might have been better appending that to the original thread.
That refers to Linux on RPi, AVR code is a bit different. I will post a cross reference, then the OP can decide whether to look at this.
OK, so it looks like that's bit-banging it rather than using e.g. SPI.
It seemed easier to just start with bit-bang. At least reading the 3 data bytes should be possible over SPI, but on AVR the last 1 - 3 clock pulses used to configure the next conversion would need to be bit-banged. Maybe I'll test SPI sometime this weekend.