How come the sun doesn’t twinkle like other stars?

Because it's gigantic and a heat source for living things lol. That's not its purpose, but please don't enjoy it like star gazing and burn your eyes out 😐

Because it's too bright for us to notice any variation due to atmospheric turbulence.  Our natural satellite doesn't appear to twinkle either but through a telescope it does shimmer.  The Sun is millions of times brighter than the brightest star.  From a sufficient distance, the Sun would twinkle - probably about thirty times the distance to Pluto.

It is too bright.  Mars, Venus, Jupiter and the Moon don't twinkle either because of their brightness.  The Stars Twinkle because of the Earth's Air and the Weak Light coming from them. If you were on the ISS and was looking at the Stars they would not twinkle.

It does, if you are some 4 lightyears away from here

The Sun is too close and too big to twinkle. The atmosphere Sam be current enough that Sun does not seem to to be steady. 

"How come..." is not proper English.

"Why doesn't..." is.

The answer is simple...it's too close to us to twinkle.