I also had this problem and the solution suggested here works fine if you have a html file with the flash object so you can modify the parameters directly. But what if you (like me) use swfobject to insert the flash movie into the page dynamically? Then you need a different approach. Here is how I solved this.
Code:
function embedChart(targetElement) {
var flashVars = {}
flashVars["data-file"] = "/chartrequest/";
var params = {}
params["wmode"] = "transparent";
swfobject.embedSWF("/res/app/flash/open-flash-chart.swf", targetElement, "100%","100%", "9.0.0", "expressInstall.swf", flashVars,params)}
The important part is params, where you can send in parameters to the flash object. Just set wmode to transparent and send it in. I also tried setting it to opaque and it works too. it seems to have the same effect. I also set the z-index on my div which hosts my flash movie to -100, like this:
Code:
<div id="chart" z-index:-100></div>
Hope it helps someone. 