– Lt. Gen. Michael T. Flynn, President-elect Donald Trump’s choice for national security adviser, has a well-established penchant for pushing conspiracy theories about Islamic law spreading in the West and the attack on the U.S. diplomatic compound in Benghazi, Libya. Less well noticed was his willingness throughout the presidential campaign to indulge in conspiracy theories about Hillary Clinton.

Six days before the election, Flynn, the former director of the Defense Intelligence Agency, tweeted a fake news story that claimed the police and prosecutors in New York had found evidence linking Clinton and much of her senior campaign staff to pedophilia, money laundering, perjury and other felonies. “U decide,” Flynn wrote in the Twitter message on Nov. 2, though it appeared there was little doubt what he thought.

Flynn’s month-old tweet is attracting renewed attention after a man fired a rifle on Sunday inside a Washington pizza restaurant that was the subject of false stories during the campaign tying it and the Clinton campaign to a child sex trafficking ring.

The man, Edgar M. Welch, 28, of Salisbury, N.C., told the police that he had come to the restaurant, Comet Ping Pong, in northwest Washington, to “self-investigate” the sex trafficking conspiracy theory, which is being called Pizzagate. No one was hurt, and Welch was arrested at the scene.

But the incident marked a violent turn in a continuing story in which the restaurant, its employees and nearby businesses have been subjected to threats and harassment because of the conspiracy theory, for which no evidence has been produced.

Despite the absence of evidence to back up the theory, some high-profile supporters of Trump have continued to spread it, including Flynn’s son, Michael G. Flynn. On Sunday, hours after the gunfire at Comet Ping Pong, the younger Flynn went on Twitter to say that until Pizzagate was proved false, it remained a story.

Michael G. Flynn is more than just a family member of an incoming senior administration official. In recent years, he has served as the chief of staff to his father, who started a private intelligence and consulting business, the Flynn Intel Group, after being forced to retire from the military in 2014.

Throughout the campaign, Michael G. Flynn served as a gatekeeper for his father, and he now appears to have a job with the Trump transition team. E-mail sent to an address at the Flynn Intel Group returned with an automated response that provided a new e-mail contact for both Flynns — and each had a Trump transition e-mail address that ended with .gov.

The Twitter feeds of both men leave little doubt about their politics — the main difference is that the son appears to have shown even less restraint than his father when it comes to spreading conspiracy theories about Clinton and her campaign.

He retweeted suggestions that Clinton and President Obama were “at the center” of the conflict in Syria and profiting from it, and suggested that both would be tried for treason if Trump were elected. He shared a fake news story that claimed hackers had found video evidence that President Bill Clinton had raped a teenage girl.

And in a Twitter message that he deleted after CNN found it in November, he questioned what was wrong with dating websites that were only for white people, saying black Americans have BET, a television network that caters largely to black viewers.

Since Sunday’s gunfire at Comet Ping Pong, Michael G. Flynn has also continued to push his support for the Pizzagate conspiracy theory, retweeting messages that say the media have sought to normalize pedophilia.

His father, though, has kept a lower profile since the election. He has not given interviews, and he has kept his Twitter postings relatively tame, posting patriotic messages on Veterans Day and more recently praising Trump’s selection of retired Gen. James N. Mattis of the Marines as defense secretary.