I know Flash can use ExternalInterface to call Javascript functions but I don\'t know if it can call applet also like that. Maybe it can be done by SWF -> JS -> Applet, and back
Yes. Sockets. Your Java applet can open a server socket, probably a HTTP socket, and Flash/Flex can post content to the socket. Your applet will have to be signed by a known CA to be trusted, but once that's done you can pretty much do what you want.