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Flynn's son, Michael Flynn Jr., vehemently defended the story, which baselessly alleged that a pedophilia ring involving high-level Democratic Party officials - including Democratic presidential nominee Hillary Clinton's campaign chair, John Podesta - is operating out of a Washington pizzeria called Comet Ping Pong.
Flynn is President-elect Donald Trump's incoming national security adviser.
The conspiracy led a 28-year-old man to bring an assault rifle to the restaurant on Sunday, police said. They said the gunman was looking to investigate the story himself.
"Until #Pizzagate proven to be false, it'll remain a story," Flynn Jr. posted to Twitter. "The left seems to forget #PodestaEmails and the many 'coincidences' tied to it."
That's when Tapper apparently began to direct message Flynn Jr. on the app, asking for one piece of evidence proving that the pizza shop was "the site of a satanic pedophilia cult." Those direct messages were posted by another user.
"Michael - the police called pizza gate a fictitious conspiracy theory tonight," Tapper wrote. "Does someone have to die before you take this s--- seriously. Spreading this nonsense is dangerous."
"I want it to be false," Flynn Jr. responded.
"It is not the site of a satanic pedophilia cult," Tapper shot back. "It is a f------ pizzeria. Show me what you're talking about that proves a satanic pedophilia cult. Your tweet is wildly irresponsible. Listen to me. You are going to get someone killed. Maybe an innocent child. For what??????"
Flynn Jr. later posted another screenshot of a DM thread with Tapper with the caption, "Want evidence??? I must've really hit a nerve."
Flynn Jr. has a government transition email, as CNN reported. Flynn also shared a similar conspiracy theory on Twitter days before the November election that claimed Clinton was involved in sex crimes with children.