Yes, your ZeClock got has a camera remote option. On the Camera Remote panel, single press BOTTOM KEY to enter the menu.
Short press TOP KEY to take pictures while the camera on your paired smartphone is on.
The key setting depends on which volume key is defined for quick camera shooting on your Android device. If it is volume + key: single press TOP KEY; if it is volume - key: single press BOTTOM KEY.
Pictures will be saved in the smartphone.
Long press TOP KEY to exit the menu.