K-Type Thermocouple, Instrumentation Op-Amp and Arduino
You need a DC path for the in-amp bias currents, for example you could ground the junction or connect one lead or both to ground through a relatively high value resistor (the thermocouple and leads are usually well under 100 ohms, so any resulting error should be minimal. 

In order to get predictable filtering you will need to add some series impedance to the thermocouple leads. Try 1K on each lead, 100nF between the leads and 10nF to ground on each input. 

You should probably think about biasing the in-amp output above ground, since it's quite possible for the "hot" junction to be at a lower temperature than the cold junction, leading to a negative voltage. You'll also want to clamp the voltage appropriately for the Arduino (read the datasheet for the MCU to get the specs- you'll also need the MCU supply voltage). 

It's usually desirable to run a bit of current through the thermocouple junction in order to detect breaks. There's a trade-off between the resulting error from that current times the loop resistance of the thermocouple probe and wires vs. the current if DC current is used. You could also periodically pulse it from the MCU to detect a broken sensor or connections, but your front end might take some time to recover.