The easiest way to empty your inbox is online with the provider. Deleting messages on your device can take times and it's not always easy. Depending on what app you're using you might be able to swipe them left and they'll just be deleted as you go, other apps pressing and holding one message enables select mode and then you can select a bunch and delete them all at once, with others you can swipe right to enter select mode.... The possibilities go on and on but we don't know what so you have, what device, how many accounts you're trying to handle, which takes me back to the easiest way is online with your account at your provider. You should be able to log into most accounts thru your browser on your device if that's your only online access. I recommend using the full web version to provide the most options.