Kavanaugh has denied Ford's and other women's allegations of sexual misconduct.
Flake announced he would vote to advance Kavanaugh's nomination to the full Senate only if the Federal Bureau of Investigation were to investigate.
Flake, the swing vote on the 21-member committee, said earlier in a statement that he planned to support Kavanaugh, saying the nominee was entitled to the presumption of innocence "absent corroborating evidence".
The Senate Judiciary Committee approved, along party lines, the nomination of Kavanaugh to the Supreme Court - with a request that the FBI conduct an investigation into sexual assault allegations before the full Senate takes a vote.
President Donald Trump ordered the FBI on Friday afternoon to reopen the background investigation of Supreme Court nominee Brett Kavanaugh.
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On Thursday, the committee listened, captivated, as Blasey Ford, a California psychology professor, declared that she's "100 per cent" certain it was Kavanaugh who tried to sexually assault her during a house party in Maryland in 1982. She likened Thursday's hearing to the proceedings years ago involving Justice Clarence Thomas and Anita Hill. "But even if the credibility of the allegation has not been established beyond a reasonable doubt and even if further investigation is warranted to determine its validity or clear Judge Kavanaugh's name, we recognize that this nomination is no longer in the best interests of the country".
GOP Judiciary Committee lawyers asked Kavanaugh about both charges during the Tuesday interview, which he denied.
Rhode Island Senator Sheldon Whitehouse asked Kavanaugh a serious of questions about something in his high school yearbook: the term "Devil's Triangle".
At Yale, undergraduates students have also rallied in solidarity with the three women who have levied allegations against Kavanaugh and to call upon the school to be more proactive in addressing sexual misconduct.
Following the vote, Coons said he and other Democrats wanted the extra week not to stall the confirmation process, but to investigate the allegations now before the committee.
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Tom Cotton, R-Arkansas, on separate Sunday talk shows suggested Feinstein's office might have leaked a confidential letter by Dr. Blasey Ford, Republicans deferred to a female sex-crimes prosecutor hired specifically to ask questions.
Protestors have a moment of silence for sexual assault victims during a protest outside Sen.
"Judge Kavanaugh I thought was frightening", third-year law student Alyssa Peterson said after watching some of Kavanaugh's testimony. "But I did not drink beer to the point of blacking out, and I never sexually assaulted anyone".
"I'll tell you, Chris, I watched the whole hearing, and a number of my Yale colleagues and I were extremely disappointed in Brett Kavanaugh's characterization of himself and the way that he evaded his excessive drinking question" and "was lying to the Senate Judiciary Committee today", Lynn Brookes said. "It should be about how you play the game".
Many Republicans say the due diligence on Kavanaugh already was complete.
The New York Times had reported the entry, along with more than a dozen others on other pages of the all-boys high school yearbook, was part of a boast by football players about Renate at the time. "The girls from the schools I went to, and I, were friends". "Don't look away from me", she said.
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Blasey Ford said the incident left her "drastically altered", but it was her "civic duty" to tell lawmakers what happened. In early July 2018, Ford said, she saw press reports of Kavanaugh shortlisted for potential Supreme Court nominees.
Gerken had said last week she could not take a position on the nomination because the school is a nonpartisan institution.