FLIRC is a USB keyboard emulator. Your computer thinks that the FLIRC is a keyboard. When you press buttons on an IR remote control, the FLIRC sees them and turns them into keyboard commands.
To program the FLIRC (using the FLIRC utility that you download), you will need to map some remote control to corresponding buttons that control JRiver MC. You will have to come up with what buttons you want to program and what keys they will send to MC.
The obvious few are left, right, up, and down arrows. Also the Enter key. Beyond that, you'll need to decide what you want. I think escape acts as a "back" key in MC's Theater View, so that would be a good one to map also.
Best of luck!
Brian.