I have a strange issue with flexslider but I also had the issue with bxslider, When I load the page flexslider will not work but if I resize the window it then works, I have added removed css/js but still the issue is there. You can see the issue here on my test server http://www.webcontrolcentre.co.uk/sitetest
if you navigate down to 'section four' you will see a link called 'view showcases' the slider is within that section.
It's a bit hard to reproduce without editable example, but FlexSlider usually has trouble initializing on hidden elements.
Does it work when you don't hide the .showcase?
You can try re-initializing the flexslider after clicking on the "show-btn"-toggle.