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The problem is inside the furnace itself... that is why the thermostat is flashing.
Please attach a well focused, close up photo of the wiring diagram glued inside the service panel, the picture needs to betaken from straight on, in very good light.
You can use the paper clip- icon at the right end of the tool bar at the top of this dialog box to attach it here. ,Include a picture of the thermostat wire connections to the printed circuit board in the same area.
If there is no paper clip-icon, look for the '+attach files'link at left of your send button.
I can mark it up with trouble shooting instructions.
You will need a multi meter ($30 at a hardware store) and some experience working with appliances, let me know a lot about your skill sets in those regards.
We can go from there.