I have 2 mechs in star spring and I charm unit to star spring. They target my mech to kill it. Can I use Akali's ability to bring the mech back to base to avoid the damage?

No — not as a reaction. Rogue Assassin's ability is [Action][T], not [Reaction], so it can only be activated in an Open state (you hold Focus in the showdown, or your own Main Phase). The moment your opponent's kill spell/ability is on the Chain, you're in a Closed state and only Reaction-timed things are legal (Rule 813.1.c.2, Rule 358.4) — you can't squeeze Akali's ability in to save the mech.

If you instead fire it while you hold Focus in that Combat Showdown (the mech is "in a showdown" there, so it's a legal target), the mech does move to Base — but whether that dodges the kill depends entirely on the other effect's wording. If it says "at a battlefield," moving to Base makes it mistarget and the mech lives (FAQ 9929). If it's a plain "Kill a unit" or a damage spell with no location restriction, the mech is still a legal target at your Base and still dies (FAQ 3724).

Worth flagging: after Charm drops an enemy unit at Star Spring, that unit applied Contested, so your opponent is the Attacker and takes Focus first — meaning they get their action window before you get yours, and they can also just respond to your Akali activation with a Reaction kill spell, which resolves first.