I am also working on the shali-fotografie.nl website. I disabled all plugins, except the GRAND Flagallery plugin and still no gallery on the mobile devices (I use Android 4.1.2). With the new versions of wordpress you can watch your website with different themes (live preview) and I checked it with some default wordpress theme and than I did see the gallery (I’m using a mobile user-agent for testing).
So the problem is the theme, there must be some javascript conflict, because I use the several .css solutions provided, but no luck. When I look at source, I don’t see the gallery being loaded. Furthermore, the theme being used has 7 different jquery files, so I’m guessing one of them is conflicting.