You can do this to save a file with curl:
$ch = curl_init($url);
$location = "video.flv";
$fp = fopen ($location, "w");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($ch, CURLOPT_FOLLOWLOCATION, 1);
curl_setopt($ch, CURLOPT_UNRESTRICTED_AUTH, 1);
curl_exec ($ch);
curl_close ($ch);
fclose ($fp);
I think that is what you wanted