Personally, I have no use for this—I rarely delete many emails, and never all of them at once—but for those who would like it, try this:
1. Go to your inbox
2. Press Edit
3. Tap any message once to select it
4. Press AND HOLD the Move button
5. While still holding the Move button, tap the message you selected
6. Release the Move button
7. This will bring up a dialog box asking you which folder you’d like to move all your messages to – just select the Trash folder and you’re all done
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Edit (source):
How to delete all your mail at once on your iPhone 4 (updated for iOS 6, including iPhone 4S and iPhone 5) | Jason Elk