Sorry I was being snarky about the kiln comment, didn't know this is what you are doing. I find it frustrating the IC is a PITA whether it's a kiln or reflow oven, a simple application but many hassles reported by people.
What I suggest for your project's success with this IC:
-I would add the EMI resistors R10/R11 and/or ferrite beads and a series resistor on BIAS pin 2, like the eval board has, to stop EMI coming in on that pin.
-The thermocouple and its wiring cannot touch anything conductive i.e. metal grill, baking pan, kiln walls, sheet metal, yourself etc. Also kept away from any mains/heater wiring.
Depending on your heater relay, they can make a burst of EMI when the contactor switches or if you're using phase-control. An on/off SSR gives quiet switching but they generate a lot of heat. So if you see problems with readings/fault-codes only whenever the heater switches on/off then you know it's the source of interference.
-This IC will not work well when powered from a two-prong AC adapter, including a laptop's USB port. The Y-capacitor adds too much CM noise. You must have an earth-ground connection to the DC power supply. Connected to a PC there is an earth-ground connection via USB but this can get lost out at the kiln when this runs off batteries.
If the thermocouple pokes out and taps the heating element, the board becomes hazardous live and is a danger, if the board is grounded then smoke and sparks will fly.
-In firmware, maybe keep two averages for temperature- a short term and a long term that does not get updated if at that moment a fault-code is set or the reading is way off. This is to reject any bad readings, and stop your software from jumping to the next stage by accident, or scuttling it's forecast. Or try only take a temp reading when the heater is pulsed off, unless it's constantly on of course. I think you can model the kiln temperature integrating the heater on-time and ballpark thermal mass inside from pottery, unless the bricks are the main mass.
The problem at high TC temperatures >900°C, the IC flakes out with fake fault codes, the Adafruit forum guy said leave it floating (not grounded) he says apparently the IC needs only 50uA of leakage current to report a fault and it's due to hot air becoming conductive? Strange voodoo that I don't believe but I don't know 900°C air.
Analog Devices "Flexible, Low Power, 4-Channel Thermocouple System with Arduino-Compatible Digital Interface"
CN0391 ahhh look a grounded thermocouple input and
CN0394 AC grounded leg, as it should be. There are many helpful TC app notes there too.