A check engine light flashing means that you have got a misfire in the engine and if the car is shaking while the check engine light flashes then you have a serious misfire that can damage both your engine and your catalytic converter.
The flashing check engine light is telling you that you need to get the car to a mechanic as soon as possible as in right then to prevent further damage of your vehicle.
If you continue to drive the vehicle with a severe engine misfire then you risk even more costlier damage.