There should be an easy way for every user to delete own Flow posts. It's possible in Facebook, Twitter, LiveJournal and Quora, and should be possible in Flow, too. Users shouldn't have to wait for an admin to delete a post that they regret submitting. Posts can be hidden, but these are still easily accessible.
I'd object to this for the same reasons I objected to the same feature in phabricator, at T1185: Rate limit or restrict access to comment removal. (Easy info-suicide. Deleting single posts would create suspicion/speculation. Admins would still be able to snoop on what was deleted.)
This would be the equivalent of granting all editors RevDeletion for their own posts. Unless there's a broad community request for a feature like this, I don't think it's something we'd encourage.
After talking with the team, I'm going to close this as declined, but feel free to continue discussing it, or start a community RfC or similar.
Many wikis, including the English Wikipedia, allow deletion requests for pages where there's a single author and the author is requesting deletion.
Deleting one's own post is probably closer to allowing an editor to revert his or her own edit to a wikitext talk page. MediaWiki page history is just about as obscure as the trash can in practical terms.
Your note declining this task doesn't seem to address the task description. The inability to delete one's own posts is in contrast with other sites (Facebook, Twitter, etc.), which raises concerns about needlessly defying reasonable user expectations.
There are compromise approaches that can be taken here, as you note in T1185. Time limits are an option. Another option is disallowing the ability to delete one's own post if the post (or perhaps the thread) has any subsequent replies. In discussions about revising MediaWiki edit summaries, I believe we largely settled on an "own, last, and recent" philosophy, which seems potentially appropriate here as well.
I basically agree with Quiddity that this needs community consensus, at least for enabling it on Wikimedia wikis. Deleting a post is much more similar to revdel (inaccessible to non-admins) than it is to reverts (still in page history). Individual communities can still allow for courtesy deletions.
If hidden posts are too prominent, that's a separate issue. The same goes for this being unexpected for users (in fact, I would argue that it's not necessarily unexpected, given many online forums also don't allow deletion of own posts).
That said, I would probably not object to this if there is a sufficiently short time limit (say 10 minutes, along with the no replies rule) to restrict the feature to quickly removing accidental postings.