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The thermostat blinks the flame icon when the compressor is in lock out due to power loss or interruption.
It sounds like your compressor is cutting off and not re energizing until the thermostat is reset again. This could be due to a short in the defrost control board of the outdoor unit or the unit could be cutting off on low or high pressure switches due to lack of refrigerant or an overheating compressor. What is the temperature like where you are and is it raining? Also what is the make and model of your outdoor unit.
you want FA for the cycle rate being that it is electric back up heat.
and you want the fast second stage on.
If you were to leave the fast second stage off then the aux would not kick in unless your heat demand call was 10 degrees or more over the current temperature displayed on there thermostat. If this is the case when the temperature's drop below 36 degrees or so your heat pump would run and run and run and run doing nothing until 10 mins later when the aux kicked in to help it.
If your thermostat is displaying EMER in the screen then you have the function slide setting set to "emer heat" instead of "heat". when in emergency heat the system only runs the aux back up strips in the furnace and does not run the outdoor compressor.