I don’t think this is possible with z-index alone because even if you could get the shadow that is assigned to “flexslider” to appear in front of your image, flexslider still has a background that would hide your image anyway?
I would try something along these lines (output from firebug). I have removed the shadow from the flexslider and created a new div for the shadow to sit in. The inline styles would go in your stylesheet-
<div class="home-slider"><div class="flexslider">
<li style="display: list-item;"><img src="http://witouchtens.nl.testbyte.nl/media/wysiwyg/slide1.jpg" alt="pijnstilling lage rugpijn"></li>
<div class="shadow" style="box-shadow: 0px -8px 10px -8px rgb(105, 104, 104) inset; height: 14px; position: relative; margin-top: -14px;"></div></div>
Hope this points you in the right direction.