So it's 16 clocks per sample. You need to output the command byte at the same time as reading in the first reply byte, then output a 2nd byte (zeros) to force anothe 8 bits of clock to read in the 2nd data byte.
Look at my gertboard.c driver in wiringPi - it's fairly similar to how that works. (the one in the wiringPi directory, not the one in the examples)
You can only read one converter though - the Pi only has one SPI port. (So you can read 2 inputs on one convertor, but not the inputs on the 2nd convertor), so connect up, Clock, serial in/serial out and one of the Pi's enable pins to the chip (CS) and I think that's all you'll need (other than the usual power, ground, decoupling,etc.) Connect RD to CONVST by the looks of it too.
You could read the 2nd convertor, but you'll need a couple of tristate buffers to enable one at a time to the Pi's MISO pin.
Simples
-Gordon