Just send them a little message saying "Hey, you've falsely reported a bunch of posts/accounts lately, so we're restricting your ability to report content for 30 days." and if they keep doing it, make it permanent.
Actual hostile actors will have years to find ways to use the rules to create controversy and shut down dissenting posts.
If people learn they get flagged after N spurious reports, they'll start rationing their reports so they don't meet the treshhold; they'll start making inflammatory posts that technically respect the rules to bait false reports. They'll create scandals, eg "Person X said awful thing Y, but when I tried to report them Facebook told me I wasn't allowed to report people anymore. Why does Facebook support Y?"
That's not to say your idea is bad. Just, you're making it sound really easy, when it's a problem Facebook has poured millions into without finding many solutions.
And flagging/vouching privileges can be removed for HN users who abuse them.
Another potential mitigation might be to put a limit on the number of posts that a single user can flag in a day. At some point, the cost of large-scale content manipulation could be made to exceed the expected gains.
It may even be profitable for Facebook to crack down on this. Every celebrity post that gets illegitimately taken down has potential for showing ads to millions of people.
HN has addressed this problem by keeping it text-only.