I absolutely agree that you were correct to flag the answer. It is effectively an upvote of the other answer or a comment. However, I'm not sure I agree on the specific flag that you chose.
Let's look at the text of the flag description (emphasis is mine):
This was posted as an answer, but it does not attempt to answer the question. It should possibly be an edit, a comment, another question, or deleted altogether
The emphasis is where "Not an Answer" seems inappropriate. This answer does address the question, so Not an Answer wouldn't seem to apply.
I might have considered selecting "Very Low Quality" but flagging this situation as "Other" and explaining the problem in brief detail would have been the best choice.
To understand why, you have to understand how moderators look at flags.
First, they normally don't see individual flags, and most are grouped by post (although I believe there are some exceptions), so when they see a flagged post, there is often not a lot of context as to why a specific post was flagged, except for the flag type.
Which leads to the 2nd point, mods do not see the post in its entirety when reviewing flags, they only see the first couple of lines of the post that was flagged. They need to click through to see the entire question and all of the answers. So when you flag something and it may not be clear exactly why you are flagging it, a moderator may not know how you want them to act and are forced to make a guess. In this case, since the answer did address the question, a moderator might not have known that this was a duplicate of a previous answer and declined your flag.
But when you flag as "Other", and explain the situation, now you give the moderator enough information to make an informed judgement on the flag and post, and be able to act appropriate.
The one thing that you shouldn't do though is use "Other" for everything. It should be reserved for cases when the reason you are flagging requires an explanation or additional information that cannot be conveyed through the flag type and reading the first few lines of the post. In cases where is it clear cut, you should select the appropriate flag type.