Am I misunderstanding the response or the declined/helpful process?
You misunderstood the purpose of flagging.
In your flag reason you wrote, "I didn't know until now that I can respond to disp[uted] flags." That is not true; what you have done is to flag again a post you already flagged, to which a moderator can reply by rejecting it, and giving a custom reason for the rejection.
Flags are not for getting a reply from moderators; flags are for letting moderators know something needs their interventions. Their reply is actually doing something with the post you flagged (e.g. lock it, close it, delete it). They give you the reason for declining it, but that is just to teach you how to flag posts; using the declining reason for answering something you asked means using the declining reason for a purpose that is different from its original one.
If you need feedback about something, you can:
- Ask on the chat room associated with the main site
- Write a comment for that post
- Ask a question on the meta site
If the flag was incorrect, how can I prevent the mistake in the future?
You should use the flags just to say "there is something wrong with the post, and it needs the attention of a moderator." If you flag a post for getting an answer from a moderator, you are using the flag for the wrong purpose.
The "very low quality" flag has been declined probably because it has been used an answer that should have been flagged as "not an answer," a question that should have been flagged as "not a real question," or a post that could have been edited. The "very low quality" flag means that is not possible to edit the post, which is not understandable as it; if the post is an answer, then it is not really an answer; if the post is a question, then it's not a real question, as in its actual form there isn't a question at all. The "very low quality" flag carries a different meaning than "not an answer," or "not a real question"; it means something should probably done with the account used to post it, such as in the case of a user account used to post no-sense as one of his/her first answers (e.g. "ddfsefser jwerjwerefr Drupal sucks 12213 sfsdfdg2 234235 245wgrsgsdfv").
If you wanted to flag the question as not a real question, you should have followed these steps:
- Click on the "flag" link
Select "it doesn't belong here, or it is a duplicate"

Select "not a real question" in the next screen

Click on "Flag Question"
flag
again and the system auto-matches to your earlier flag. It appears however, that older disputed flags drop off the list and I'm not sure how to get to those without scanning all the questions you've ever reviewed on the site.