Is it permissible for a Muslim to say the supplication, "O Allah, if I have reviled any believer, then make that a means of closeness for him to You on the Day of Resurrection" for one who has reviled another, and is this supplication specific to the Prophet (peace and blessings be upon him)?

The oppressor cannot use the supplication of the Prophet, peace and blessings be upon him: "O Allah! Muhammad is but a human, he gets angry as humans get angry, and I have made a covenant with You which You will not break: any believer whom I have harmed, or cursed, or whipped, make it for him an expiation and a means of proximity, by which You draw him closer to You on the Day of Resurrection." This is because this supplication is specific to the Prophet, peace and blessings be upon him, as he made a condition with his Lord concerning it. What emanated from him was not oppression, but rather anger for the truth. Whereas, the oppressor must seek forgiveness from the oppressed, or seek forgiveness for him and improve his treatment of him in his absence.