I think you're absolutely right, but there are two problems.

First, why should human flourishing be the standard of value? Why? Sputtering around saying stuff like "put your hand on a hot stove!" only tells me that (1) Harris fundamentally doesn't understand Hume's objection and (2) I'm reminded that I'm not a masochist and being burned hurts so I will essentially involuntarily not want to do it. Involuntarily disliking having my hand badly burned is not a reason. So...why? Harris never actually tells us.

Second, given what he chose ("human flourishing"), there are already a host of questions about its coherence as a goal. Present people vs future people? Do numbers of people alive matter? How many transcendent experiences listening to Beethoven's 5th make up for one hand on a hot stove? That is, it's got all the usual utilitarian flaws (some of which Ben pointed out)--and it is not at all obvious what the answers are if you pick a distributed goal like "human flourishing". If you pick a non-distributed goal like "it goes like D. Trump wants" then, sure, any time you have a tricky decision you ask the authority. But optimizing distributed value is tricky when it comes to people since most naive attempts admit unspeakably barbaric actions and/or extraordinarily counterproductive ones.