Why does it say "Malchei Yehudah"? There was only one king!
Radak: This refers to the king and his sons. Since his sons would rule after him, he called them kings.
This refers to the leaders. He should warn them first. (So implies Malbim - PF.)
Why does it say "that they enter through it
Malbim: Warn them several times, when they enter and leave.
Why should he go to different gates?
Radak: First he should go to the gate where the kings of Yehudah enter and leave, for they should rebuke the people and guard Shabbos. Not only the kings enter and leave there, rather, also the nation who dwelled near that gate; he should call also to them. Afterwards, he should go to all gates of Yerushalayim to warn the entire nation. Hashem told him to call in the gates, because people enter and leave through them on Shabbos. He warned them only about Hachnasah and Hotza'ah via the gates to [or from] outside the city, for they were not liable for carrying in the city, for the doors of Yerushalayim were locked at night, so it was not Reshus ha'Rabim (Eruvin 6b).