How can I delete multiple emails at once from the iPhone 6?

If you are referring to the inbox, you can only do that by selecting Edit, then select each of the mails you would like to delete and then tap on the trash can. There is no ability to "select all" and then delete. If this is an IMAP or Exchange account, the easiest way is if you have access to the account via a computer and can delete multiple mails that way.