Flash inserted through the html_flashobject method is inserted using the <object> tag and conditional comments. This is the recommended way to insert flash in the most XHTML valid way.
Unfortunately the <object> is not supported by Google Reader and possibly other RSS readers.
There are three possible solutions:
1. Add the invalid embed tag when embedding Flash (and lose support for alternative content)
2. Let the feed creator replace Flash <object> tags with <embed> syntax
3. Keep it broken
Not sure which one is the best way to go. Maybe others have a 4th solution?