Here is a workaround until Apple restores the Select All - Delete functionality in iOS 10:
1. Open the inbox you wish to delete all
2. Tap edit (top right corner)
3. Tap to select any email (this will enable the move functionality)
4. Tap & Hold "Move" (bottom center)
5. While holding "Move", tap to de-select the email from step 3 (you are doing this so all emails, not just the selected email get moved)
6. Release "Move" (this will bring up a list of destinations to move your mail
7. Tap "Trash" or "Archive" to move all messages to the respective destination
It's convoluted, but a workaround nonetheless.