Tomasz,
Flash has worked for me in a ruby webdialog on the mac. We use it in the Get Photo Texture extension, for example.
How are are initializing your flash movie? Are you using javascript to create the <object><embed> tags? Or manually writing them into your html? If you're using JS, it might be trying to detect that flash is installed or some such, and getting confused about which browser it is running in.
Simple test: create a WebDialog and point it to some public websites that run flash, like Streetview or YouTube.
The JS code that has worked for me in the past is something like...
<body onload="onLoad()">
<script>
function onLoad() {
var path = 'myMovie.swf';
var html = ['<object classid="clsid;d27cdb6e-ae6d-11cf-96b8-444553540000" ',
'codebase="http://download.macromedia.com/pub/shockwave/cabs/',
'flash/swflash.cab#version=9,0,0,0" ',
'id="flash">',
'<param name="allowScriptAccess" value="always" />',
'<param name="allowFullScreen" value="false" />',
'<param name="movie" ',
'value="', path, '" />',
'<param name="quality" value="high" />',
'<param name="scale" value="noscale" />',
'<param name="swLiveConnect" value="true" />',
'<param name="salign" value="lt" />',
'<param name="wmode" value="transparent" />',
'<param name="bgcolor" value="#ffffff" />',
'<embed src="', path, '"',
' quality="high" scale="noscale" swLiveConnect="true" salign="lt"',
' wmode="transparent" bgcolor="#ffffff"',
' style="position;absolute; z-index;5"',
' name="myFlash" align="middle" allowScriptAccess="always"',
' allowFullScreen="false" type="application/x-shockwave-flash"',
' pluginspage="http://www.macromedia.com/go/getflashplayer" />',
'</object>'];
document.getElementById('someDiv').innerHTML = html.join('')
}
</script>
Let me know if that helps. It could be some security stuff, too, but let's start with this...