Record an eye blinking waveform signal from EEG signals
You can't. 


Flatline EEG is how brain death is defined, and while it may be possible to induce an eye blink in a deceased human, I am sure ethics will not approve, and it won't be scientifically satisfactory. 
even in the case of a real flatline EEG, there will always be some remaining residual activity (albeit very weak), such as line noise. 


However, 


the eye blink is a few orders of magnitude stronger than the ongoing EEG
you can isolate eye blink activity using techniques such as ICA