I wound up using this. It is a kind of a hack, but it actually works pretty well.
The only thing is you have to be very careful with your semicolons. : D
var strSql:String = stream.readUTFBytes(stream.bytesAvailable);
var i:Number = 0;
var strSqlSplit:Array = strSql.split(";");
for (i = 0; i < strSqlSplit.length; i++){
NonQuery(strSqlSplit[i].toString());
}