Apple sure does not make it easy to delete multiple emails on iOS, which can be a real pain in the neck if your automated alert system spams you with say 4000 messages in a 2 hour period over the weekend link mine did recently. Off site with no access to my Outlook client I was annoyed to say the least. It took a LONG DANG TIME to delete all those messages from my iPhone, but it would have taken a lot longer if I had to swipe and delete each of those messages individually.
Unknown to many, iOS does have an admittedly klunky way to delete large amounts of messages. Here it is with easy to use pictures of each step.
1) Open your email client (duh)
2) Tap "Edit" from the top right side of the screen
3) Scroll along and tap the messages you would like to delete - a red dot will appear next to the selected messages in those little empty circles.
4) Tap "Delete" to remove the selected messages.
Presto! You have just batch deleted messages under iOS. The same technique works for all of them. You would not believe how long I went without knowing how to do this.