Story highlights Retired Lt. Gen. Michael Flynn has pushed false news stories on his social media accounts

Virginia Sen. Tim Kaine is taking issue with him and a few other Donald Trump Cabinet picks

(CNN) Virginia Sen. Tim Kaine intensified his criticism over Donald Trump's national security adviser, saying that retired Lt. Gen. Michael Flynn peddles in conspiracy theories that even a little child would dismiss.

Kaine, who was Hillary Clinton's running mate this year, has kept a low profile since suffering the stunning loss to Trump last month. But Kaine told CNN Thursday that Flynn lacked the judgment to serve as Trump's top adviser on national security issues.

"The general I'm worried about is Gen. Flynn," Kaine said in an interview. "Gen. Flynn's trafficking in conspiracy stories that a fourth grader would find incredible suggests either that he's highly gullible or that he's so consumed with malice that he loses his ability to judge what's fact and what's fiction."

Kaine added, "Having a national security adviser who has demonstrated either such gullibility or such malice in charge of offering advice to the President on the critical national security issues of the day, I think, is highly highly troubling."

Kaine was referring in part to Flynn pushing false news stories on social media, including that Clinton was involved in a child sex ring.

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