Tap the "Mail" app.
Tap the name of the email inbox you want to bulk delete email from.
Tap "Edit" in the upper-right corner of the screen.
Tap the small white circle to the left of any email messages you want to delete from that email account. A red circle with a white checkmark appears inside of the white circle.
Tap "Delete" in the lower-left corner of the screen after you have selected all the messages you want to delete. These messages will be removed from your iPhone.