Chapter 36 says Sai Baba can turn a beggar into a king. Is this meant literally, and does it also mention him being an incarnation of Lord Vishnu?

Chapter 36 uses metaphorical language to describe Sai Baba's immense power and grace. The phrase that he can "turn a beggar into a king in a moment with the play of his eyebrows" is meant to illustrate his infinite glory and ability to change a person's fortune, likely both materially and spiritually. Regarding the second part of your question, the text does not state that Sai Baba was an incarnation of Lord Vishnu. Instead, it says he was one who "attained Lord Vishnu (Chakrapani)," which implies he achieved a state of God-realization, and through that attainment, he helps redeem others.