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"I hear that General Mike Flynn has offered to testify if given immunity. What does that mean?"
A grant of immunity is how a prosecutor gets a witness to testify if the person might otherwise invoke their fifth amendment rights. Immunity says: even if you incriminate yourself, we will not prosecute you based on your testimony.
But what happens when there is more that one potential party who can grant immunity? Right now there are three investigations into Russian interference in the 2016 election: the FBI, House Intelligence Committee, and Senate Intelligence Committee. Reportedly, Flynn made the offer to all three — to testify in exchange for “immunity from prosecution.”
If one entity grants immunity it can eliminate the ability of the others to prosecute. For example, during the Iran-Contra hearings, Congress gave Oliver North immunity from prosecution in order to compel him to testify over the reservations of the independent prosecutor. (The prosecutor then separately convicted him of destroying documents, accepting an illegal gift, and aiding and abetting in the obstruction of Congress; but those convictions were later overturned.)
Reports today that Senate Intelligence turned down Flynn's offer to testify. No word from the FBI or House Intelligence.
Does a request for immunity mean someone is guilty? No. It means that they perceive there is a risk that their testimony could lead to prosecution. In this case, Flynn’s lawyer cited the politicized environment as his reason to seek immunity.