Here is how you do that in Java:
Object args = ...
String sourceName = "my.cfc.path.Component";
RemotingMessage message = new RemotingMessage();
Object returnValue = amfConnection.call(null, message);
and accessing the body of the response like this.
Object body = ((AcknowledgeMessage) returnValue).getBody();
Not that the "args" variable is an array of the arguments you are passing to the CFC function. It can also be a Java List, or a simple object. See the BlazeDS source for RemotingMessage.java for details. This sends the same kind of message that the mx:RemoteObject tag does in MXML, so in ColdFusion terms you are using the "Flash Remoting Update". If you use the 'raw' AMFConnection API, you would be using the "classic" Flash Remoting. Both will work, but I recommend using the RemotingMessage style.
What does this do for you? Well if you are exclusively using Flex as a client, not much. But if you would like to write Java code to invoke a CFC, this alows you to do that very easily.