Can I spend Sett Brawler's Buff on my opponent's turn?

No, you cannot spend Sett, Brawler's buff on your opponent's turn.

According to the FAQ for Sett: Brawler (#7445): "Ruling: The ability is standard speed, meaning it can only be used on your turn outside of chains or showdowns. All effects without ACTION or REACTION keywords are standard speed, and there are no effects that can be used 'whenever'."

Because Sett, Brawler's ability ("Spend my buff: Give me +4 might this turn") does not have the [ACTION] or [REACTION] keyword, it is considered a standard-speed ability. Standard-speed abilities can only be activated during your own Action Phase when the state is open (i.e., when there is nothing on the chain).