My 2006 Dodge Neon service engine light started blinking, the car stalls, and starts back up. What might the problem be?

Check for codes. It might be, for example, a bad Crankshaft Position Sensor or Camshaft Position Sensor.

Usually a flashing check engine light means an emgine misfire so bad that the results could damage the catalytic converter.
Have the codes read and let us know what those codes are.