The problem is that flash is sending the data in different encoding. From the comments in the PHP manual for mb_convert_encoding I can see that you should use the following to get it to work (tested on danisch charactors and not greek)
<?php
$string = isset($_POST['xmldata'])?$_POST['xmldata']:"";
$filename = isset($_POST['filename'])?$_POST['filename']:"";
//tested on danish chars
/*
$string = mb_convert_encoding($string, "ISO-8859-1", "UTF-8");
$filename = mb_convert_encoding($filename, "ISO-8859-1", "UTF-8");
*/
//tested on greek chars
$string = mb_convert_encoding($string, "ISO-8859-7", "UTF-8");
$filename = mb_convert_encoding($filename, "ISO-8859-7", "UTF-8");
$path = "test/";
//$dir_handle = @opendir($path) or mkdir("{$path}", 0777, true);
file_put_contents($path."/".$filename."", $string);
?>