There will also be issues with the conductivity of the probe and flame, and your 1K resistor might be a bit much, if the probe's resistance is high enough. Measure the resistance, and use Ohm's law to find the power drawn. You want to make sure the power is below the max for the arduino, but high enough to register. If the voltage is dropping too much to register, or the current is too high and tripping protection or something, it wouldn't work.