Move? Never.Fly? Yes.
And to be exact, LS was not reached instantly in a heart beat I believ it was reached, which is still slower than the time it takes to process a thought (around 20 milli-seconds)
Jean is not the Embodiment of the Phoenix, she's an Avatar like the rest, just the most powerful Avatar.
I'm sure Jean can fly as fast as she wants, but I believe she processes information like any other regualr Mutant or Human.
When Jean was conversating with "the consciousness" during the infamous #154 issue, she seemed kinda dumb even, nbot what one would expect from a Cosmic Intelligence, why would her thought process be any different.
Something like that.
I've simply never seen any version of Phoenix doing Speed feats on that level.
Has Phoenix?
Atleast Wanda got Shot in the Heart, by Hawkeye no less, precision accuracy and survived.
Jean croaks at the hands of,
Xorn, KILLING Jean Grey the White Phoenix of the Crown with an Electromagnetic Pulse
Wolverines Claws killed her once and some Shiar Lazer took the life out of her, it didn't disintergrate her, or re-wrote her DNA, but she died.
Jean isn't that smart, her brain is not Cosmic, it took her half the Comic book in #154 to figure out she just had to change the past.
Which again proves that Wanda is FAR beyond her in power, because Wanda Remade TIME several times, and Jean needed the White Hot Room plus she had to go back in TIME and change Scotts mind to aalter the Future.
While Wanda was Altering everyone's Future with a thought.