On Drupal Answers, there have been an answer for Is Drupal appropriate for what I want to do? that has been flagged with a custom reason, and then deleted by its author. As result, the flags were automatically handled, and none of the moderators were probably able to see the custom flag.
Automatically handling flags such as "very low quality," or "not an answer," makes sense, as once the post has been deleted, there is nothing left for the moderators (which eventually would delete the flagged posts).
There are other flags that are about the post, and the user who posted it: A spam flag is about the post, but it also about the user who can be a potential spammer. The same can be said about a custom flag: There are cases where a user needs to flag another user, and the suggested action is generally to flag a post written by that user.
As the custom flag could be about the user, it is probably better not to automatically handle them, or at least notify the moderators in some way.
If doing this for every custom flag raised against a post deleted by its author is not convenient, it should at least be considered for those posts with other flags, including comment flags. In this case, there were three "rude/offensive" flags for three different comments.