Save your flash file .swf in this location -> NopCommerceStore folder / images / thumbs
Now go to admin section > Content Management > Topics
Find "HomePageText " and click on "Edit"
now in the while space provide > you will see 3 button at the bottom > click on this [<>]
and paste this code for flash:
<object width="550" height="400">
<param name="movie" value="http://www.myamericanfurnituregalleries.com/images/thumbs/YourFlashFile.swf">
<embed src="http://www.myamericanfurnituregalleries.com/images/thumbs/YourFlashFile.swf" width="550" height="400">
</embed>
</object>
now save it (Just change "YourFlashFile.swf" with your flash file name)
For inserting images > you can use image tool on the tool bar available on this HTML EDITOR
save it
and you should be able to see the flash on your home page...