This information comes from iDropNews.com in this article: http://www.idropnews.com/6-ios-9-tricks-you-didnt-know-your-iphone-could-do/
This refers to Gmail in the instructions below. This works if you had added your Gmail account to the native Mail app on your phone or iPad. It does NOT refer to the Gmail app itself.
Do you need to purge all of your emails in one quick motion? Apple’s new operating system upgrade has now made this possible. The new iOS 9 has a new feature that will let you immediately erase all your mail in the Mail app. If you are using Gmail then you should start by changing the archive setting to delete by:
- Going to Settings
- Open up Mail, Contacts, and Calendars
- Select your account
- Go to Advanced
- Under Move Discarded Messages and select Deleted Mailbox
- After you do this open up the Mail app
- Select Edit at the top
- Click TRASH ALL at the bottom
Voila! Now your email is completely empty! You can now enjoy the benefits of having an inbox with zero emails.