The SharePoint 2010 page editor allows you to edit the raw HTML for a page with one huge caveat: it strips out anything it considers unsafe. Including object tags you might use to embed a flash video.
There are quite a few articles / forum posts online with workarounds that either don’t work, or are far too complicated for the average power user.
Then I found this blog post:
Adding Flash Content to SharePoint 2010 / Office 365
While I don’t usually post about things other have already figured out, for some reason Bert’s article took me quite a while to find.
I will be posting a simplified version of his steps for use with the vzaar video hosting service soon.