Both plugins I like and are easy to work with yet they don't work together. Installing the two together means that FlexyTalk (FT) seems to override the Cookie Control (CC) button. I assume one is high jacking the JS of the other but I cannot find it. To make things slightly more complicated the behavior varies in different browsers.
This page (http://fernleafconsulting.co.uk/FLWP/live-chat/) has a custom template and should be the only one where FT is visable. But you will see CC icon is removed from other pages. [note: This is true in Safari but in Chrome the CC icon disappears and reappears depending on the state of FT]