I've taken a step backwards to reconsider everything here.
I've just viewed both your galleries (http://www.grantsymon.com/e/start.html and http://synonyms.pagesperso-orange.fr/test/index.html) in Chrome 39.0, Internet Explorer 11, Firefox 25.0.1, Opera 26.0 and Safari 5.1.7 and do not see the flickering/double-loading problem in any browser. This suggests that the problem may not be web-server related, although the only way I can replicate such a problem is by adding a 'no-cache' directive to a web server. (This is why I mentioned the Cache-Control header in the first place but if this was the root of the problem, then I should be able to see the problem in WebKit browsers of my own.)
I do not know if tackling this problem from scratch will help, but it might.
Could you please confirm which browsers you currently see the problem in? (Is it only in Safari 8 or also in other browsers, too?)
Do you see the problem in this test Juicebox-Pro v1.4.3 gallery which uses imageTransitionType="CROSS_FADE"?
http://juicebox.net/demos/pro/default/? … nLoad=TRUE
If you do see the problem in this test gallery, then the problem may be related to either Safari 8 generally or perhaps just your own browser. If you have any extensions installed in your Safari browser, try temporarily disabling them. Also, try resetting all your browser settings to their default values.
Please post the URL to your WowSlider gallery and I will let you know if I see any flickering in image transitions in any browsers.
If I do not see any flickering, then the problem may somehow be unique to your own system/setup.
Also, if you like, you could email me one of your galleries and I could temporarily upload it to a different web server to see if this makes a difference. If you are agreeable to this, then please let me know and I will send you an email address where you can send me the gallery.
Maybe tackling this problem from a few different angles will help track down the source of the problem.