Design review for photoresistor-controlled linear regulator
My suggestion is to drive the fet with a phototransistor instead of an LDR. They have much higher sensitivity (change in resistance versus illumination) than LDRs which should minimize the flicker dramatically and you wouldn't need the opamp circuit at all in my opinion. Though, using a schmitt trigger is still a good idea to have a defined signal at medium illumination.
You can just arrange the phototransistor in series with a pull-up resistor to drive the FET (or the schmitt trigger respectively).