Can a unit get when I attack triggers multiple times? E.g. I move in, get struck trigger, use an effect to move back to base, and in same Showdown in a new chain back into the same combat?

No — in the same combat, that unit's "When I attack" trigger fires only once, even if it leaves and re-enters.

Attack triggers are checked once per combat per unit (Rule 383.4.e.2.a). Moving back to base and re-entering the same Showdown/combat means the unit regains the Attacker designation, but the condition is not re-checked for that combat. New chains within the same Showdown don't reset anything — the combat is still the same combat.

The trigger would activate again only if the combat ends and a new combat starts (e.g., the showdown fully resolves and a later move opens a fresh combat at a battlefield), or if the unit arrives late to a combat it hadn't yet gained Attacker in. It also can't be "banked" — you can't trigger once, leave, and come back to get a second use out of it.