Mail on an iPhone

Try this.

Go the mailbox that you want to delete all messages from.

In the upper right hand corner, select 'Edit'.

Tap on one of the circles to put a blue check mark next to one message. You only need to select one.

Now touch and hold the 'Move' button at the bottom of the screen. Hold it, do not release.

While still holding 'move', uncheck the message you checked in the step above.

Now release 'Hold'.

On the following screen select 'Trash'.

All messages will be moved to the trash.