If the coil feels hot to the touch after its been working then it is probably getting intermittent.This is a common problem for dryers with a little age on them coils. When this happens the coils shut down for a long period of time. But then will work a little bit and quit again. Very aggravating to diagnose. Replace them. Onward to the flame sensor. I have seen the bi-metal inside them get stuck for long periods of time. The gas assembly comes on and off all during the drying process. So it gets worn out and starts to stick. You should go ahead and replace that flame sensor. All components are energized when the heat is called for. The ignitor, the flame sensor, and them coils. The coils will not open the gas unless the resistance in the circuit changes. To do that the sensor and ignitor must drop out of the circuit. The average time a gas assembly stays on is around a minute or untill the drum gets to 160f. Then the control on the blower housing next to the fuse shuts off power to the gas assembly and the drum keeps a trucking till the temp dops to 105 f at which time the gas valve assembly is again energized. This cycle continues till times up clothes no longer are wet depending on whether or not your dryer has a dryness board or a simple autodry feature.