As I understand it, Pence can’t raise executive privilege for his discussions with the President, because executive privilege is controlled by the current President, not a former President or a former V-P. So what he and the Donald chatted about just before the Donald tried to get the mob to hang him isn’t privileged.
He successfully relied on the “speech and debate” clause, because when he went into the chamber to count the electoral votes, he was exercising a legislative function, which is a separate protection:
“…for any Speech or Debate in either House, they shall not be questioned in any other Place.”
The text actually just refers to Reps and Senators, but the V-P is in an unusual position because he has legislative functions (tie-breaking and counting electoral votes), so I guess the clause applies to him? (Just speculating; haven’t seen the decision.)