In the details, you did not state if the flame would come back on in a minute or two. If the flame comes back on and then back off after ten seconds the problem is most likely a venting problem. A simple test is to pull the dryer out and disconnect the vent. Start the dyer without a load and see if the flame stays on. If the flame stays on the problem is venting. If the vent is short, you can clean it with a shop vac. if you have a long vent you might have to call a vent cleaning company to clean the vent.
If the flame does not stay on the problem could be a few different things. The burner has a thermostat on the top that will turn the flame off it gets to hot. The dryer has a flame sensor that detects the flame. The flame sensor is not a high failure part.
If the flame goes out and does not come back on the coils are most likely the cause of the problem. I have provided you with the instructions for accessing the dryer below. If you need further assistance, please submit more details.