It is not possible to display a WP-Juicebox gallery multiple times throughout a WordPress site.
Each WP-Juicebox gallery is linked to an individual post and displays the images attached to that post.
(You would need the ability for the gallery to display images attached to a different post.)

You would need to upload the images for each gallery.

If you want to reuse images, then you might like to consider using a different source for your images (such as Flickr, a NextGEN Gallery or a Picasa Web Album). You could quickly and easily set up two different galleries to display the same images in these cases.

It is not possible to duplicate a gallery created by WP-Juicebox.
You could reuse images (but not a gallery) if the source of images is Flickr, a NextGEN Gallery or a Picasa Web Album but if the gallery is sourced by Media Library images, then, no matter where the images are stored (locally or on Amazon S3), you will need to upload the images again and attach them to the post containing the new gallery.

You could, however, create a gallery on your computer with JuiceboxBuilder-Pro and use the baseUrl method of embedding (documented here) to embed the same gallery in multiple different posts.

Essentially, once you have created a gallery with JuiceboxBuilder-Pro, you would upload the complete gallery folder (not just the contents) to your web server and paste the baseUrl embedding code into the body of your WordPress post (ensuring that the method of entry is 'Text' rather than 'Visual'). It does not matter where on your web server you upload your gallery folder to as long as the two paths in the embedding code (the path to the 'juicebox.js' file and the baseUrl itself, pointing towards the gallery folder) are correct.

You can use the baseUrl method of embedding in a WordPress site just fine (similar to the instructions for Drupal and Joomla). This has none of the restrictions that using an iframe would have.

Essentially, once you have created a gallery with JuiceboxBuilder-Pro, you would upload the complete gallery folder (not just the contents) to your web server and paste the baseUrl embedding code into the body of your WordPress post (ensuring that the method of entry is 'Text' rather than 'Visual'). It does not matter where on your web server you upload your gallery folder to as long as the two paths in the embedding code (the path to the 'juicebox.js' file and the baseUrl itself, pointing towards the gallery folder) are correct.