Please let me know, what is the inbound port range that chilkat FTPS uses in the Client machine.
Chilkat FTPS is used for the client side of the FTP connections (just like the popular FileZilla). It used one outgoing connection for the control channel (sending commands, receiving OK/Error responsed) and one for sending and receiving data.
Most FTPS servers are set to receive commands on port 990 or 21 (but it can be anything). Your firewall probably allows this traffic (firewalls do not care about OUTGOING traffic).
The data connection depends on how you set the Passive property. If it is on, the client (your program) opens another connection to the ftp server. Again, the firewall will not mind (it is an outgoing connection). If the Passive property is off, you have what is called an Active connection. The FTP server opens the data connection to the client, most firewalls find this highly suspect and will block the connection or prompt the user if it should be allowed.
Anyway, look at the ActivePortRange start and end properties and the Passive property of CkFtp. I found some more background info here: http://serverfault.com/questions/10807/what-firewall-ports-do-i-need-to-open-when-using-ftps