Understanding slow response of multiplexed thermocouples
If you read the datasheet, the conversion time of that chip is 100ms maximum. It effectively samples the input voltage then goes off and does a conversion and cold-junction compensation. 



Offhand, I don't see any number indicating how long the valid voltage must be present at the inputs before doing a conversion. You may be able to overlap acquisition and conversion to some degree (perhaps start a conversion, wait 50ms then switch to the next channel, then you could immediately start a new conversion after 100ms for 10 channels/second), but that's not entirely clear from my skimming of the datasheet. In any case you can't do any better than 100msec/channel (reliably) though some samples of the chip may be a fair bit faster.