Yes, you can use any slider jquery plugin you wish, but to feed the slideshow you need the photos.
Galleries in WordPress are composed of posts with post_type attachment, and attachments that are attached to a post have that posts ID as their post_parent. So to get the images for the slideshow or slider, you need to find posts, that are of post_type attachment, and are children of the current post.
This article has more information on attachments:
http://digwp.com/2009/08/awesome-image-attachment-recipes-for-wordpress/
If you browse to the bottom of the article there is code to grab all the attachments attached to the current post:
$args = array(
'order' => 'ASC',
'post_type' => 'attachment',
'post_parent' => $post->ID,
'post_mime_type' => 'image',
'post_status' => null,
'numberposts' => -1,
);
$attachments = get_posts($args);
if ($attachments) {
foreach ($attachments as $attachment) {
echo apply_filters('the_title', $attachment->post_title);
echo wp_get_attachment_link($attachment->ID, 'thumbnail', false, false);
}
}
This can be used as a basis for generating the markup for the slideshow/slider by modifying the html in the post loop.
This question deals with using nivoslider and image attachments: