Попробуй autoplay="true" добавить:
<object classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" id="letplayer" codebase="http://fpdownload.macromedia.com/get/flashplayer/current/swflash.cab" height="360" width="640">
<param name="movie" value="//moevideo.net/swf/letplayer.swf?_=3107201402">
<param name="quality" value="high">
<param name="allowScriptAccess" value="always">
<param name="allowFullScreen" value="true">
<param value="file=77806.7dbeed54f45c4c3bba67303ec325" name="flashvars">
<param name="wmode" value="opaque">
<embed allownetworking="all" id="flashfirebug_1406995351567" src="//moevideo.net/swf/letplayer.swf?_=3107201402" quality="high" bgcolor="#000000" name="letplayer" play="true" loop="false" autoplay="true" allowfullscreen="true" allowscriptaccess="always" type="application/x-shockwave-flash" flashvars="file=77806.7dbeed54f45c4c3bba67303ec325" wmode="opaque" pluginspage="http://www.adobe.com/go/getflashplayer" align="middle" height="360" width="640">
<param value="all" name="AllowNetworking">
</object>