As I'm sure you're aware, there is no actual limit to the number of galleries you can have on a site (or a page) but finite resources in a real world scenario could prove to be a restrictive factor.
Unfortunately, every server is different (with different limits) and each user's galleries are different (with different numbers of images at different filesizes) so it's really difficult to give you a number as to how many galleries is too many.
Having said that, if you only have one gallery per page, then there really shouldn't be a problem at all.
The browser will just be parsing one page at a time (as and when they are viewed) and, thus, only one gallery will be consuming resources at any one time. Galleries on other pages should have no bearing on this problem.
As far as I can see, a problem regarding gallery numbers would only occur if you were displaying multiple galleries on a single page, (i.e. multiple galleries were all being loaded at the same time and many images would be preloaded at once).
Do you maybe have any plugins which preload web pages throughout your site before they are viewed (maybe preloading pages which are linked to from any particular page)? This could potentially cause a large server load (loading a lot of gallery pages in the background).
I notice that you already use imagePreloading="NEXT" in your galleries, preloading just the next image rather than all the images on the current thumbnail page (PAGE) or all the images in the gallery (ALL), so that's good. There's no need to change that.
There's really no other gallery confirmation options you could change that would help with such a problem.
Storing your images locally (instead of using Flickr) might make a difference but I realise that it would be a mammoth task to switch over to this method of image storage (and, to be honest, I really don't know if it would help... it's just something you could theoretically try).
Check your plugins, though. There's may be something there that's contributing to the problem.
As I mentioned above, if you only have one Juicebox gallery per page, then there really shouldn't be a problem (at least where Juicebox galleries are concerned).