What did Zimri do when he saw that Omri's army had captured the city of Tirzah?

Answer: Burned the palace down on himself

When Omri besieged and took Tirzah, Zimri went into the citadel of the royal palace and burned it down over himself, and so died.

“Then Omri and all the Israelites marched up from Gibbethon and besieged Tirzah. When Zimri saw that the city was captured, he entered the citadel of the royal palace and burned it down upon himself. So he died”— 1 Kings 16:17-18 (BSB)