No need for a relay here...
Connect the flashing LED between a constant +12v (or something you find at +12v with the ignition off) and something that goes to +12v with the ignition on. You should find that the latter connection will have enough of a path to ground to run a simple flashing LED (with resistor). With the ignition on the LED won't flash because both ends of the LED will be at the same potential (+12v).

You should be able to do all of this on the back of the ignition switch.