Optimizing ext. SPI ADC for speed and verify the speed
Don't use digitalWrite().
Don't use delay().
Don't flood your Serial connection with useless junk ("analog value =")


You may also consider using lower level SPI operations instead of the SPI library, which is completely blocking and slows you down. At least consider the use of SPI.transfer16(...) which is more efficient than two SPI.transfer(...) calls.