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I have 500 karma and I don't see a UI element to try to vouch for it.

You can't vouch for stories. You'd have to contact the mods by email.

I have 1556 and can't either. Contacted them by email. They did unflag it :)

You can vouch for stories. It works the same way as for comments: click on the timestamp to go to its page, then click 'vouch' at the top (https://news.ycombinator.com/newsfaq.html#cvouch).

Vouch links only show up when a post is [dead], though. In this case there were enough flags to show [flag] but not enough to kill it.