How to use in a custom form?

FYI: Managed to do this manually with the following code. Doing it this way also means you can use the extra features of the spectrum color picker (like rgba colors) that color_field doesn't yet support.

In your theme's theme-settings.php:

function mytheme_form_system_theme_settings_alter(&$form, &$form_state)  {

  // Add spectrum color picker js and css. See http://bgrins.github.io/spectrum
  // Requires libraries api and spectrum installed in libraries/bgrins-spectrum
  // as per color_field install instructions
  drupal_add_js(libraries_get_path('bgrins-spectrum') . '/spectrum.js');
  drupal_add_css(libraries_get_path('bgrins-spectrum') . '/spectrum.css');
  $spectrum_js = 'jQuery(".spectrum-color-picker").spectrum({
    showInput: true,
    allowEmpty: true,
    showAlpha: true,
    showInitial: true,
    showInput: true,
    preferredFormat: "rgb",
    clickoutFiresChange: true,
    showButtons: false
  });';
  drupal_add_js($spectrum_js, array('type' => 'inline', 'scope' => 'footer'));

  // Spectrum color picker field
  $form['myform']['color'] = array(
    '#type' => 'textfield',
    '#default_value' => theme_get_setting('color'),
    '#attributes' => array('class' => array('spectrum-color-picker')), 
  );