What is the prescribed punishment if one kills their slave intentionally?

Killing of a slave is haram. Their blood is sacred like any other muslim or dhimmi and can not be shed without a legal right.

If one kills his own slave, then there will not be any Qisas. That is because the owner is both the murderer and the guardianheir. Being the latter he has the responsibility and right to take Qisas yet he can not take revenge from himself nor can he forgive himself.

Instead, the state will administer a ta'zir, and there are different madhabs on its nature:

• He will be killed.

  من قتل عبده قتلناه

  Whoever kills his slave, we will kill him

  ^{— Sunan ibn Majah}

• He will not be killed but punished.

  قتل رجل عبده عمدا متعمدا فجلده رسول الله صلى الله عليه وسلم مائة ونفاه سنة ومحا سهمه من المسلمين

  A man killed his slave deliberately, so the Messenger of Allah (ﷺ) gave him one hundred lashes, banished him for one year, and cancelled his share from among the Muslims.

  ^{— Sunan ibn Majah}

He may also be liable to pay Kaffara for murder as in 4:92 and this is stated in a version of the above hadith:

أن رجلا قتل عبده متعمدا... وأمره أن يعتق رقبة

A man killed his slave deliberately, so the Messenger of Allah ... commanded him to free a slave.

^{— Sunan al-Kubra al-Bayhaqi}