I don’t think there’s a way to hide a specific post without also resolving the flag using the API at the moment.
As an work-around, would it be reasonable if any flag automatically hid the post? There’s a site setting called hide_post_sensitivity — if you increase that to high, that drops the hiding threshold low enough so a single flag from a TL3+ user will hide the post.
You could additionally use the API to add an additional flag from a high trust user, which could increase the score high enough so every flag results in the post being hidden.