There are a couple of things that you need to think about.
First, what do you mean by the "next" gallery? You will need that value to populate the link to the next gallery.
The slideshow can take an argument of the gallery ID, which will limit the images displayed to one gallery. You can then create another view which takes that argument and displays a field (which is a link to the "next" gallery).
You can filter by node type, order by whatever you want to order by, limit to display only one node (of type gallery), and, finally, filter by the same thing you are ordering by, but use the filter to limit the list to what is appropriate, ie, do not display nodes with node id greater than (or less than) or equal to that of the argument, so you don't get a duplicate.
Then you attach that view to the gallery view, and you have a link to the next gallery. You may be able to do something with an Ajax module if you don't want the page refresh.
I'm actually having a similar problem. The issue I'm having is that I want to display the latest gallery (my galleries have a CCK date field). I can do that, but I want to limit by gallery id. However, I won't have the gallery ID because I'm displaying the "latest" gallery, so I can't just do a simple filter by gallery id. I can sort by the date, but I can't seem to limit the results to the same parent gallery without the gallery id argument. Any ideas would be greatly appreciated.