It depends on the time taken for the processor to use SPI to request a reading from the 7298, set up the 6 to 1 mux, take the reading, and communicate the answer back to the processor. That all takes time. You will not get a million samples a second on that sort of single-reading process.
If you want to get a million samples a second from the A/D converter, you would have to some other arrangements for communicating on a continuous basis , which would enable that to happen.
I don't need a million samples per second, but 10k or even 1k samples per second would be much better. Is there any way to increase the conversion speed by using a "multiple-read" rather than single-read process?