It makes sense that I can delete my own question/answer if I think that it's not a good post. It also makes sense that I can edit it to improve it. But why would I flag my own question/answer?
To request moderator action.
Anything that you cannot do yourself but moderators can do, is fair game. If you realize you asked your question on the wrong site, for example, you can flag it to request a migration.
Another reason to request moderator attention is if another user is causing problems; dealing with conflicts is best left to the moderation team as well.
Off the top of my head, if someone repeatedly vandalizes your post, you can flag it for moderator attention. Or anything that requires moderator attention, for that matter.
One good reason is if your question gets closed. It happens very frequently that a question will be asked with very little information and/or a bad description and it will be closed as "not a real question", if this happens you can clean it up fix the problems and then flag a moderator to help reopen your question.
Besides requesting assistance/moderation for vandalism and edit warring or to request closure or reopening (or deletion/undeletion) under situations where you believe a moderator would want to act, another somewhat common reason someone may flag one of their own posts with a custom flag reason is to request that many obsolete comments be removed.
This is often a preferable alternative to flagging all the comments individually, especially if it would not make sense to remove some of them while leaving others (so individual comment flags might not be clear), or if the number of comments to be removed is pretty big.
Of course, this is often a reason to custom-flag someone else's post, too. It's just not any less applicable when it's your own.
There's also a whole slew of less common but legitimate reasons to custom-flag one's own post:
- It's how you'd request one of your own questions be manually converted to community-wiki (in the uncommon but not nonexistent situation where that makes sense to do).
- As Sha Wiz Dow Ard pointed out there, it's how you'd ask for your post to be un-CW'd (though this, too, only infrequently makes sense, as usually when a post has become CW, it should stay that way).
- As Mad Scientist mentioned there, it's how you'd ask a moderator to contact Stack Exchange about removing a revision from the revision history (which is only rarely appropriate, but would make sense if something like your social security number were accidentally posted).
- As Caleb pointed out there, flagging your own post is how you'd request that it be migrated to another site.
I've listed a few reasons here since this appears to currently be the master "why flag your own post" question on MSO and those other questions might or might not be seen by curious searchers.
I flagged my own post as a duplicate when a commenter linked to a post I had missed during my initial search.