Have you assigned the throttle axis to the throttle command in FSX's controls options?
The good news is that something happens when you move the stick, so it's probably configured to talk to your PC just fine. You just need to assign the axis. You might also need to calibrate them via Windows' calibration tool.
Note that if the PS3 controller is still hooked up, you have to verify which controller you're configuring in FSX, as it's happy to recognize multiple controllers at the same time. If it's set to the PS3 controller when you're trying to assign the T.Flight's throttle, it won't respond.