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.
The Senate does not vote on whether to confirm the national security adviser spot, but Kaine suggested Flynn should step aside.
"I think he's demonstrated that he doesn't have the judgment for the job," Kaine said.
A Trump spokesman could not be reached for comment, but Flynn has been strongly supported by top Republicans on Capitol Hill who say his deep military experience makes him well-suited for the spot.
In the interview, Kaine was also critical of Trump's pick of Oklahoma attorney general Scott Pruitt to run the Environmental Protection Agency, pointing out that he's denied the existence of man made climate change.
"I'm very troubled by that," Kaine said.
And Kaine would not say if he would support a waiver for Trump's pick of retired Gen. James Mattis to run the Defense Department, something that is needed for certain former military personnel to hold the top civilian post. He said "my gut tells me" that he'd be comfortable with Mattis, but added his support for the waiver is "going to depend on conversations that we're going to have."
Kaine has previously said he would not be a candidate for president in 2020, and on Thursday expanded on his thinking. Kaine, who is up for reelection in 2018, said he wanted to say in the Senate "for a long time" -- as long as he keeps getting reelected in Virginia.
"You've got to know yourself and know where you're likely to make the most good," Kaine said. "And in assessing things in the aftermath of the election I just decided I really want to dig in here."
Kaine added: "In some ways, while I haven't figured the whole election out, one of the things I have figured out is I think I'm supposed to be here and maybe I'm supposed to be in the Senate more for the work I would do with the president of the other party even more than for a president of my own party."