Bottom flesh radical (the radical form of 肉, visually identical to 月 moon but distinct in meaning) - anchors 肖 to the body/anatomy family alongside 胃 stomach, 肝 liver, 胆 gallbladder. Here it stands for 'the flesh of a child' born from the parent.
Top three-stroke small-variant of 小 sits above the flesh radical, giving the picture of 'a small piece of flesh' - a child resembling a parent in miniature form. From this came the verb sense 'to resemble' and the noun sense 'likeness, portrait.' The same top appears in 当, 尚, 党.