There is a Lightbox feature built into the gallery which makes this very simple. A Lightbox behaves in the same way as on online shopping cart. You add images you want to your lightbox by clicking the Add to Lightbox icon above the image, or the Lightbox this Gallery! icon in the gallery header to add the entire gallery.
When you are ready to download your images, click the View your Lightbox icon on the main screen of the gallery. Here you will be able to download a ZIP file of all the images you have chosen.
HINT: Use the lightbox to create a zip file of all your personal images from the Instant Galleries, then use the Upload Media function in the User Menu to upload your zip file to your own personal gallery.