I have messages in my GMAIL account, but I cannot see any way to delete them all at once. For my other email accounts there is a delete command in the menu that when you press it gets you to a further menu to choose all and delete all.
In your gmail inbox, you should see gray checkmark boxes next to each email. If you check them, they turn green. Once you have check the ones you want to delete, press delete in the menu at the bottom. Let me know if this helps.