It is possible to delete all emails from the Inbox in the Mail app. First, mark all emails read.
Then tap Edit at the top right. Mark the first email. Tap "Move" at the bottom and hold your finger there, don't let go. Uncheck the first email again and lift soir finger. The account will show you the amount of emails in the Inbox (Inbox will be greyed out), and you will see all your Mailboxes of the account. Select the one where you want to move the messages, in your case "Trash". Done!
View attachment 17724
View attachment 17725