What exactly happens (or does not happen)? Is an error message displayed (or is anything displayed)?
If nothing is displayed at all, then perhaps the problem is due to JavaScript being disabled in the browser or viewing the gallery over a 3G connection (rather than wi-fi). If 3G is being used, then please see this FAQ:
Why can't I view my gallery on a 3G mobile connection?
If the problem is simply due to a slow internet connection, then the problem may be due to the browser timing out whilst trying to load files. Certain browsers may allow you to change the timeout parameters (such as 'network.http.response.timeout' in Firefox's 'about:config' section) though not all browsers may have such settings and I cannot be certain that changing them will even help (though it might be worth trying).
Unfortunately, there is no way to change the way that Juicebox loads images from Flickr.