It's a bit of a tangent, but is downvoting or flagging on a site like HN a threat to free speech? Maybe it restricts speech on HN, specifically, but then we would be separating the more traditional understanding of "free speech" (linked specifically with government intervention) from another one (like the happenings in a private forum such as HN).

I do downvote people I disagree with on HN, that seems like simply a low-effort way of registering one's opinion. Flagging I think of as being intended more for abusive, as opposed to just unintelligent, statements. Certainly, if someone abused the tool to flag everyone who expressed a certain opinion, that would be suppressing free speech. Whether the government would be obligated to intervene would likely depend on whether the owners of HN would like the suppression to stop.