This is not a SWFObejct related issue, but how the browser is cahing your old content. You either need to configure your server to send the correct headers on when a file has been modified, or you can bludgeon the browser into thinking you are requesting something new by tacking on a unique querysting to the file.
So lets say the file you changed is called some.swf.
if you update that swf with new content, then you could insert it into the html page with a location like some.swf?v=1.
The browser will treat some.swf and some.swf?v=1 as different files, and you will see the new content straight away.
Now, what if you want it to be a new file EVERY view? Well, you can tack on a dynamic identifier onto the end of the file using something like the below (which will give you a millisecond accurate unique number for you file). Every time the page is refreshed, the file will be downloaded again as a new file:
"some.swf?v=" + new Date().getTime();
Hope that helps,
Aran