Which champion gets Reach for the Stars as a hero augment?

Reach for the Stars is a hero augment for Jax.

Is Reach for the Stars a reroll hero augment?

Yes — Jax is a 2-cost champion, so Reach for the Stars fits reroll comps that 3-star Jax.

Gold augment

Gain a Jax. Your strongest Jax becomes a Magic Fighter that deal bonus magic damage on attack and gains stacking Attack Speed on cast.

Attack Speed

Bonus Attack Speed makes a unit attack more often per second, which means more auto-attack damage and faster mana generation toward the next ability cast. Some carries scale beyond that — their ability itself fires more hits when they have more Attack Speed (e.g., Bel'Veth's slash count, Jinx's rocket count). Stacking AS items and traits on these units compounds: faster autos, faster casts, and bigger casts.
On Cast

This effect triggers the instant a unit casts its ability. Items like Lich Bane and Innervating Locket reward you for landing as many casts as possible.
Stacking In Combat

The carrier ramps power within a single round — Titan's Resolve gains AD/AP per attack or hit taken, and Samira builds toward The Groove on knock-ups. All in-combat stacks reset when the round ends, unlike takedown-stacking which carries across rounds.