When my gas furnace goes on, the flame will be on for twenty seconds then turns off for about 5 seconds. The flame then reignites and repeats this cycle until the heat kicks off. The blower is running the whole time, just the flame turns off and on until temp. reaches desired thermostat temp. Is this off/on flame cycle normal??

Not normal.

If you have a flame sensor clean it.

Make sure all registers are open

Make sure nothing is blocking the return air openings

Make sure the air filter is clean.

Does your heater make a loud noise when the flames goes out? Mine is doing the same thing as your heater is. But when the flame goes out it makes a loud sound, like the flame spoofed out, loud air blowing sound.