Aside from a few inter-tribal skirmishes, the Second Battle of Sitka in 1804 is likely the last time Tlingit battle gear was used in combat.
Warfare changed rapidly after contact between Alaska Natives and Europeans. Armor could sometimes deflect a musket ball, but the better weapons shattered it. Heavier layers improved a warrior's odds but slowed him down.
By the time of the Battle of Sitka, the Tlingits were using guns to repel the Russians. Firepower determined the outcome. The Russians had cannons and the besieged Indians' dwindling supply of gunpowder was a key factor when Tlingit leader Katlian -- who owned several guns himself -- decided to organize an evacuation of the defenders to a safe location.
Russian leader Alexander Baranof also wore armor, a vest of chain mail right out of the Middle Ages. He may have been the last person on Earth to wear such antique protection into battle.
... Much of the old Tlingit armor, of no further use to its owners insofar as fighting was concerned, was brought out for special occasions well into the 20th century.