One more note, and I am done for now. If you go to PWM control to drop the current on the gas control solenoid, you should add a low pass filter to the circuit to smooth the voltage and current through the solenoid. You can use the inductance of the coil as part of the low pass, but it will benefit from parallel capacitor with a low value inline resistance. You can find designs for PWM solenoid control on the web. The values for the parallel capacitor will not be critical, it just needs to be in an appropriate range for the inductance of the solenoid coil. Some designs do not use a series resistance on the capacitor. It depends on the transistor you are using as a driver. Peak current into the capacitor on initial startup can damage the transistor, and a low value series power transistor will limit that peak current. Your transistor choice will determine the design of the filter. The smaller the capacitor, the less the peak current and duration.

The RC snubber approach is good for an AC circuit where you can not use a freewheeling diode. It protects the switch (contact or semiconductor). In a DC or PWM (no polarity reversal) circuit I definitely use a freewheeling diode with the coil inductance as filter alone. Together it works like a step down converter (lower coil voltage and lower input current). The voltage is pulsed, the current slowly decays while it flows through the diode. Solenoids have generally high inductance, so you don't need a very high frequency to stay in continuous conduction mode where the current does not decay to zero. This has less losses than the RC circuit.

The approach with a secondary shut of MOSFET is good. You can do this with a capacitive coupling (like a charge pump) of the solenoid drive signal to it's drive stage. So its is driven only while the arduino produces a valid dynamic (PWM) signal. Or you drive it with an external watchdog which must be triggered by the arduino in regular intervals (several 10ms). If the program gets stuck, the WD times out and the gas valve gets forced shut (power off).

One other thought, the gas heater that I owned had a thermocouple in the gas line that prevented the gas from flowing unless 1) the standing pilot was lit or 2) the burner was lit. There was an override button that you had to hold down until one of those two states existed.

Does your heater not have a thermocouple on the gas valve?

nope, a thermocouple is not present. As you can see in the video above where I test the flame sensor, you just turn the knob to get the gas going.

I like the idea of replacing the large resister by using PWM control from the Arduino, as mentioned by Martin. I also agree that you should stick with Arduino for this type of embedded design, just from a stability point of view.

Adding a couple other thoughts, if you cycle the gas off after it has been running for some time, you will have to continue monitoring the flame sensor for a while, because those ceramic blocks will signal that the flame is lit for some time after the gas has turned off, because they glow so hot. I used to have one of these heaters, so I am familiar with how they work.

If you don't wait, you could turn the gas back on and think that the panel was burning, when you are just registering the hot panel. So don't allow the gas to flow again until the panel has cooled enough to see the flame sensor return to a negative state.

I may have missed it in the description, but are you running the spark all the time? Or just until you get a positive indication from the flame sensor?

In any case, for safety reasons, you should add a main MOSFET control on your gas valve that is not controlled by the Arduino, but is driven directly from a buffered output from the flame sensor and also from a filtered output of the coil driver. On the low side of the coil, you can run a diode with an inline current limit resistor to a small capacitor driving a buffer stage. The buffered output from the flame sensor and the buffered output from the filtered coil driver can be run through an OR gate to drive the MOSFET in the gas valve driver. In that way, the gas valve cannot open in any case unless either the spark ignition is on and running, or the flame sensor detects flame. With this as just transistor logic outside the Arduino, you get an extra level of safety to protect against coding or microprocessor errors. So even if the Arduino fails with the gas valve driven open, a loss of flame, or the spark turning off, will also shut the gas valve.

thanks for taking interest and excellent feedback. I will revise the hardware and update here with my findings. I plan to run the spark only to to start the fire, not continuously.

If the flame sensor really "sees" the hot panel, than I would try to change it's position. Normally theses sensors should be UV detectors, not IR (heat). If it is not selective enough then Doug's strategy with waiting for cool down is necessary. Then I would think about a longer time out of several minutes to limit the rate of thermal cycles of this heater. 

But basically it's true: If you do not expect the flame to burn, then the correctly working sensor has to deliver a negative (no flame) signal. Otherwise something is wrong. Which means stop this after one or two retrys give an error message and do not continue without manual user interaction. The primary goal is to reduce danger.

the sensor I have detects wavelengths between 760 nm to 1100 nm (near infrared)

"sensor I have detects wavelengths between 760 nm to 1100 nm" 

that's not so good, it WILL see the bright glowing heating element very good. Better than your cell phone (or most other digital) camera. Because these normally have a IR blocking filter to reduce (not eliminate) IR sensitivity.

So you have to test for the sensor not seeing a flame, before starting the next igintition and heating cycle.

Please view the first video embedded in this project page with title "Keyes flame sensor with Arduino" It is a good demonstration on how fast the sensor reacts when fire is started and then turned off.

@Asad, reaction speed of sensor: 

OK, this is really very quick, so no real issue. Still I would do a check for "no flame" before ignition and "flame" after ignition. If there is no flame 5s or 10s after ignition then shut down to avoid possible accumulation of flamable gas in the room.

@Martin Yes, I agree.

Other comment: The choice of a microcontroller  (arduino) instead of a raspberry pi is very good from a standpoint of safety.  It is more reliable and deterministic.

Only if you are really paranoid. I would use a series resistor to the gate and make sure there is good grounding.

thanks for taking interest and thoughtful feedback.  I will revisit the hardware.

your spark plug ground should connect directly to the negative terminal of the ignition coil. the way it's shown in the diagram, once the pulse is removed the voltage will build up on the primary and secondary as the magnetic field collapses, and the voltage spike will probably travel through your +12v rail to get back to your power supply ground and to the spark plug, since the primary coil is the path of least resistance and the negative of your coil is now isolated since the mosfet is off. also, you might want to add a flyback diode to your coil if you run into any problems with burning out mosfets. weakens the spark somewhat though.

You should use a HV capacitor across the primary and a a MOSFET with a rating of several 100V. Similar to old style contact point ignition.  With a flyback diode the spark can be very weak. The induced voltage in the primary adds up to the transformed secondary voltage. If you limit it by a diode you severely limit the secondary voltage.   Ensure also good supply decoupling (electrolytic from 12V to Gnd.

The ignition coil has normally a dedicated HV output. You can not change this connection arbitrarily. Normally the voltages (supply, primary and secondary) add up this way.

You use an arduino. This has PWM outputs. So there is no reason to waste so much power in your current limiting resistor. Just drive the solenoid valve with a 100 to 200Hz PWM signal and you can regulate the current to any value you desire. You need just one MOSFET instead of two. Only one thing: don't forget the freewheeling diode!

So you can give it a punch to kick in for - lets say - 30ms and reduce the current as low as possible for reliable holding. As the solenoid has inductance there will be recirculating current through the diode. This saves even more power. You can measure it once and determine the correct PWM duty cycle. If you want you can even compensate for varying supply (battery?) voltage if necessary. You can easily measure the voltage with the arduino's ADC inputs: You need a voltage divider with an impedance of 5 to 20 kOhm and a filter capacitor (around 100nF to 1µF).

It would also be more easy to drive the solenoid with a NMOS FET in the low side line. You would not need any level shifting. WHICH I MISS ANYWAY in your drawing. If you connect the arduino to the PMOS FETs like you draw, then the FET will probably never shut off. The arduino's output signal varies between 0 and 5V and the gate source voltage of the FET varies between 7V and 12V, both is way above the threshold.

Your solenoid valve looks like it is made for water (which cools it also). is it also rated for gas?

The same I have to say about your use of a 555 timer circuit: use a timer output of your micro controller!

if he replaces the 555 timer output with an arduino IO pin I would recommend he uses an opto-isolator to protect the arduino.