You didn't yet answer the questions in your previous post related to the same topic.
I'm not motivated to study MSP430 details, some more comments may be helpful for those who aren't familiar with it.
In the present code:
- you are not waiting for conversion ready
- I guess, UCB0TXBUF = 0x00 is triggering a SPI byte transfer. If so, is it correct to start a second transmission without waiting for end of the first?
- did you check correct SPI mode setup according to AD7366 requirements