Why do you need a flash player to show youtube video? If no specific reason then, Just put this:
<object width="425" height="350">
<param name="movie" value="http://www.youtube.com/v/HvHOCqbA6rE">
</param>
<param name="wmode" value="transparent">
</param>
<embed src="http://www.youtube.com/v/HvHOCqbA6rE"
type="application/x-shockwave-flash" wmode="transparent"
width="425" height="350">
</embed>
</object>