Are you emailing the files? If so, the client may need to download attachments into a folder first, then open html to view. If they see the Adobe Flash warning message, they will need to activate or update Flash.
What am I doing wrong, do i need to send the SWF file with the html file? HAAAALP!!!
You probably want to give up on SWF as a presentation format.
The export creates an HTML wrapper which loads the swf and its assets. For that HTML file to be viewed locally the linked assets have to stay relative to the HTML file, the user has to have the Flash plugin active, they can't be on a mobile device, and in most cases the SWF still will not load locally for security reasons. For the HTML wrapper to correctly load a swf the files really need to be loaded on a server, so your only hope would be to upload the HTML and swf to your web server and provide a URL.
client needs an interactive "page-turning" booklet
No they don't. They WANT one.
There really is no good reason to use SWF for this and long list not to. As already pointed out SWF requires flash player to be installed and that is most certainly something you cannot count on. It also will not work on any mobile device.
There are plenty of better ways to do this including PDF.