Maybe because Flash files are not a Microsoft format, integrating them into PowerPoint is a bit tricky. Here is how to do it. Make sure that the .SWF file is in the same directory as the PowerPoint file. Click on the images for a larger picture.
When sending the presentation via email, it is best to ZIP the 2 files (PPTX and SWF) into one document. Still there is a high risk that the receiving party will not manage to see the Flash animation correctly. Do not use this for the critical slides in your deck.
Thank you Karin Mazor for pointing this out to me.