As HHS Secretary, RFK will appoint members of the CDC's vaccine advisory committee ACIP. So he can appoint anti-vaxxers to that important advisory committee. He can also modify the advisory committees' charters.
He can also overrule the FDA and CDC on vaccine approvals and recommendations. And change the criteria for vaccine approvals and reviews.
He can't unilaterally ban all vaccines and removing an approved vaccine from the market has statutory legal protections, but he can still cause incredible harm to our ability to access vaccines.
Ultimately his biggest harm will be with the bully pulpit. He can greatly undermine public trust in vaccines and our health agencies.