In the Yahoo!7 Dating Mailbox, you cannot delete individual messages, only individual Connections with users with whom you are no longer communicating.
To delete Connections from your private Yahoo!7 Dating Mailbox:
To delete multiple Connections, check the checkboxes in the left margin of the Mailbox home page for all the Connections that you would like to delete. Then simply click the "Delete" button. You can then review the Connections that you have chosen to delete, and, if you choose, even send them a pre-written Courtesy Reply. Go ahead, do the right thing and let someone know if you're not a fit… They'll appreciate it—and you would, too.
After you delete your Connections, they appear in Trash. To permanently delete your messages, empty your Trash by checking the Connections you wish to permanently delete and clicking "Permanently Delete."
Note: After you permanently delete a message, we cannot retrieve it.