Where is the flame sensor for my coleman dgaa090bdta furnace?

That's how it should work .Your furnace will cycle on and off to reach set point .
You don't have to troubleshoot the thermostat. The reason why your furnace cycle is once the heat exchanger get to a certain temperature the board will shut it off, fan would still work to cool heat exchanger down then once cool down furnace will fire up again .

replace the flame sensor,looks sorta like this,http://www.ebay.com/itm/Coleman-Furnace-Flame-Sensor-7975-3881-7975-388P-A-DGAT-/370453130096?hash=item5640ba2b70

Is this a blend air system? If so, there is an upper & lower control board that communicate to each other, and if the exhaust fan on the roof is out, it will give you intermittent issues. The fan mixes or blends outside air with the return of the air handler, & duals to pressurize the attic. These were installed due to mobile homes built too air tight. Without this fan, your roofing shingles will curl, and your roof decking will bow prematurely.

That's a coleman brand furnace and the four blinks of the green LED light indicate that the lower limit switch is currently open which would indicate an overheating issue. This would cause the gas valve to not open and thus no flame and no heat. Likely, the switch is just bad and needs to be replaced. Here is a source for the switch: http://www.hvacpartstore.com/2409.html . The switch is located right next to the electronics control panel un the upper section of the furnace. You can try turning off the power and taking the switch out and tap on it a few time or try to flex the snap sensor a little bit on the back side. That might get it working temporarily until you can get a new on. Just don't try to bypass the switch or modify it all since it is very necessary for saftey.

If its a High Eff. Furnace, does it have a two pipe or
single pipe system?

Clean the flame sensor with a green scotch brite pad. Check all ground connections from the circuit board to the furnace cabinet. Check for a proper ground to the electrical box. Make sure polarity has not been reversed.

if you know what the flame sensor is try gently cleaning it with sandpaper they get gummed up sometimes and don't sense the piolet flame, if they don;t see a piolet it will not allow it to kick the gas on

This sounds like a bad heat exchanger. It is possible that you do not see the crack because the crack is closed when the heat exchanger is cold (or room temp). Allow the furnace to heat up, this will allow the expansion of the crack. Turn the power off and examine the heat exchanger while it is still hot.

Sounds like the flame sensor. But it could be the thermostat. Is the furnace standing pilot or electronic spark or hot surface ignition. I would start by checking thermostat. Turn power off to furnace take thermostat off wall and take wires marked r & w and connect them together. Turn power back on if furnace works then change out thermostat.Most eclectronic ignition Furnaces have a flam sensor, You could take flame sensor out and clean it up with steel wool or wire brush. If you need anymore help just reply back .

is the air filter clean afc could be dirty