Car starts rough and check engine

The flashing Check Engine light is the most serious and means stop the engine right away. Too much raw fuel is going into the exhaust system where it is going to overheat and damage the catalytic converter. The place to start is by having the diagnostic fault codes read and recorded. The people at many auto parts stores will do that for you for free, but understand those codes never say to replace parts or that they're bad. They only indicate the circuit or system that needs further diagnosis, or the unacceptable operating condition.