Not all n infact most flip cover will not unless is made to be so. If your flipcase is advertised having such a feature than go ask for replacement

Only the original Samsung SView cover has auto lock/unlock when you close and open the flip, and it works great since I'm using it now. There's a magnet in the flip and authentication chip in the back for this to work.

The original Samsung standard flip cover does not have such feature.

You can install apps like Gravity Screen to enable quite similar functionality by using the Proximity Sensor.