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The flashing is a time delay.Lets allow it to flash for 5 minutes and see if it turns solid cool and comes on.If not we will go from here.
OK will fan run without blowing fuse in FAN ON position?
OK that tells us we have a short in the control circuit to the outdoor unit, in thermostat or wiring in between.If you can get some extra fuses and want to troubleshoot this by trial and error, I will be happy to guide you.About the easiest way to find the short is eliminating one possible cause at a time until we find what is blowing fuse.
Let me know and we will go from here.