Stars twinkle due to tiny variations in the earth's atmosphere. A star appears so small to us that even one tiny dust particle gettinng in the way can make the star blink out, just for the tiny fraction of a second that its light is blocked. The net result of dust particles and variations in the refractive index of the air is to make the star dance around, and also vary in brightness.
A star is so far away that it always appears as a point, even seen through a telescope with high magnification. A planet is much closer, and is seen as a disc even through a low powered telescope. When a dust particle intercepts the light coming from a planet, it only blocks a fraction of it. The brightness of a planet, averaged over the whole disc, doesn't vary much. The planet does still dance around, but again the effect is very localised. If you view a planet through a high powered telescope you can see one or more features of the planet move relative to the rest.