How does a flame sensor work in home furnaces by using a metal rod in the flame?

Its not a flamesensor its a pilot generater it generates a small amound of electricity to open the main valve that way if your pilot light goes out it wont let gas escape and couse a potentian explosion

The above answer is not accurate unless you have a standing pilot model furnace. Then the "flame sensor is called a thermocouple, much different than the flame sensors used in Direct Spark Ignition, hot-surface and intermitant ignition furnaces.

The flame sensor uses the flame of the main burner to prove flame at the circuit board by measuring conductivity to ground through the flame.