This will chew through all the pages within Cloud App's web interface, and delete all files.

cloud_app_file_delete.js

// Run in console.
(function ($) {
  var checkbox = $('#select-all-drops')
  var select = $('#actions-select').find('select')
  var button = $('#choose-action')

  function f () {
    if (!checkbox.is(':checked')) {
      checkbox.click()
    }

    if (select.val() !== 'delete') {
      select.val('delete')
    }

    button.click()
  }

  setInterval(f, 5000)
})(jQuery)