Is it considered disbelief to go along with someone who jokingly said, "I will become a prophet," and does inner rejection of it bring salvation, and what is the best way to make him understand that his statement is an act of disbelief, along with the proof?

Your boss's statement that he will become a prophet or a minister after finishing his work at the company is a slanderous statement and mockery of religion. There is no prophet after Muhammad, peace and blessings be upon him, and whoever claims prophethood after him is either a denier of the Quran and Sunnah or a jesting person, and both are disbelief and misguidance. A Muslim must denounce mockery of religion and leave the place if the perpetrator does not respond. Smiling or laughing upon hearing such a statement makes its owner a partner in sin if it is done out of consent. The duty is to repent from negligence in denouncing evil. Joking with something that involves disbelief or فسق (transgression) is strictly forbidden.