Passing boolean values with wp_localize_script

Try this:

$options = get_option( 'theme' );

wp_localize_script( 'flexslider', 'flex_vars', array (
  'flex_auto' => ($options['slide-auto']) ? 'true' : 'false',
  'flex_animation' => $options['slide-animation'],
  'flex_direction' => $options['slide-direction']
) );

Assuming slide-auto is the option you made a boolean.

This script isn’t tested, I directly typed it in here.