The Prime Minister, Mikhail Mishustin becomes acting President. Russia has laws covering this.

I'm not sure where he could flee to, though.

Or, perhaps more realistically, decides to go nuclear?

Watch this now, to learn how to take care of yourself in that event. The odds aren't as bad as Hollywood makes you think they are.

  Let's talk about fallout from the unthinkable....
  Beau of the Fifth Column
  670K subscribers
  https://www.youtube.com/watch?v=ox8ZDbCNTCE