I have made a few helpful flags since joining MSE but I've never bothered to follow up the posts I flagged. But just recently I flagged this answer for not making any attempt to answer the associated question (not an answer) and it was deemed helpful. I visited the answer today and it was still there. My question is what happens to flagged posts or to be precise what happened and/or will happen to this post?
All flags cause a little ping to appear to the moderators, similar to the notification box that every user has. A better analogy would be the suggested-edit-review counter at the top - available for multiple people to see.
For generic flags, like closing as duplicates and not-an-answers, users with sufficiently high reputation (> 10000) also can see a flag notification bubble at the top. You can read more about this on the privileges explanation section. Users get the chance to go ahead and say whether flags are valid/invalid. I don't know what the other mods think, but this process really helps me when I am going through flags.
But some flags are only visible to the mods. In particular, flags with custom messages do not appear to users with access to moderator tools, but instead only appear to the mods themselves.
I don't feel comfortable talking about the specifics of any flag in particular, but to respond to your question about that post, a moderator reviewed the flag, thought it was helpful, and has taken an action. Sometimes, mods work on a slightly slower timescale than the rest of the internet (I certainly do - for example, often for new users, I might send a message about the content of a post, suggesting that they change/improve/edit/delete a post, and then give three whole days! for something to happen).