All you should need to do is make sure the actual Web page where the Flash is embedded includes the following lines of the View Cart code in the page's HTML -- these lines are required to generate the cart-overlay display from that page:
<script language="javascript" type="text/javascript">
<!--
function EJEJC_lc(th) { return false; }
// -->
</script>
<script type="text/javascript" src="https://www.e-junkie.com/ecom/box.js"></script>
...and also make sure your Flash content is embedded as "transparent", so the cart can "show through" the Flash when it's displayed (this prevents the Flash player from covering up the cart display). This is described at the top of the Flash help page I linked previously.