Embedding a SWF in WordPress is historically a bit of a pain. The software doesn't allow you to directly embed a SWF like you would if you were editing the HTML yourself, so like a lot of other things in WordPress you need to use a plugin. This walkthrough will show you how.
Visit the URL below and download the Kimili plugin which allows you to embed SWFs in WordPress entries:
http://kimili.com/plugins/kml_flashembed
In a WordPress entry, include the following:
[kml_flashembed movie="http://yourdomain.com/path/to/slideshowpro.swf" height="400" width="600" base="." /]
Modify the movie attribute with an absolute URL to where your published slideshow SWF lives. Also modify the width and height if necessary. The base attribute is included to override the Flash Player's default behavior of making all content paths relative to the HTML document the SWF is embedded in. By including this, we make all paths (like XML File Path) relative to where your SWF is, so if your XML file is constructed with relative paths the links should work from anywhere.
Publish the entry and try it out. If it doesn't work, try launching the Safari web browser and opening the "Activity" panel from the "Window" menu. It will show you if there are any path errors, which should provide a good clue into what's breaking. Also check your plugin installation to ensure that it is installed and active.