I've played Kubb with people who keep a very strict order to who can throw when, but the rules you'd play with in the largest tournaments don't force you to keep track of that.
If a player on the team has batons to throw, they can throw them.
Some teams will strategize around this and have certain players who "specialize" in King shots and "Clean up". You'll see settings for that in the Planet Kubb Wiki.
I personally don't pay much attention to who throws when and would probably have the second player take their king shot in that scenario, followed by the third player, but no one would make you play it that way.