Why would you need to bind a FTP clients ip to the gateways/firewalls ip? PASV is a RPC generated port range defined and instanciated by the ftp server for the client to use.
FlashFXP isn't ftp. It encapsulates ftp as part of it's peering/remoting service as well as supports traditional ftp. But binding a client doesn't do anything for you unless it's FlashFXP on both ends.
Sounds like you have 2 things confused with each other. As with pure ftp, binding any of your ports to your public IP won't do a lick of difference under windows or linux if the server is configured wrong. All you can do is disable PASV and hope for the best. (with FlashFXP I believe what might have made it work for you is because you were remotely telling the other deamon to transfer to you, instead of you requesting transfers from it)
But I believe there are Linux FlashFXP alternatives. I saw some java application that supported it once, but don't remember anything about it. Just type FlashFXP in google using this;