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[1].
Unfortunately the <object> is not supported by Google Reader[2] 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?
[1]
http://latrine.dgx.cz/how-to-correctly-insert-a-flash-into-xhtml#toc-final-solution
[2]
http://www.google.com/support/reader/bin/answer.py?hl=en&answer=70664