Request: Skype Icon

As the documentation says, you could include the icon in your functions.php:

function storm_social_icons_networks( $networks ) {

    $extra_icons = array (
        'skype' => array(                  // Enable this icon for any URL containing this text
            'name' => 'Skype',               // Default menu item label
            'class' => 'skype',              // Custom class
            'icon' => 'fa fa-skype',          // FontAwesome class
            'icon-sign' => 'fa fa-skype' // May not be available. Check FontAwesome.
        ),
    );

    $extra_icons = array_merge( $networks, $extra_icons );
    return $extra_icons;

}

add_filter( 'storm_social_icons_use_latest', '__return_true' );
add_filter( 'storm_social_icons_networks', 'storm_social_icons_networks');

And be sure you allow links using the skype protocol. Also in functions.php:

function custom_allow_skype_protocol( $protocols ){
    $protocols[] = 'skype';
    return $protocols;
}
add_filter( 'kses_allowed_protocols' , 'custom_allow_skype_protocol' );

Cheers.