How long after the DUI charge can be expunged in New York and should Miranda rights be read on a DUI arrest?

No Miranda: The remedy for not being read your rights ("Mirandized") is that any admissions found to be involuntary that you may have made to the police cannot be used against you. It does not mean an automatic dismissal of the charges against you. The police know this so they don't bother Mirandizing you if they don't need your statements or a confession to prove your guilt. No expungement: I am sorry to be the one to tell you that there is no expungement in the State of New York.

There is no expungment in NY State and Miranda rights have nothing to do with what you are asking in any event. It's like mixing dirt and steak.