We moved your post to the Legacy area as the Motif ES as this is more appropriate.
The L/R audio outputs of the Motif ES should be connected to audio interface. If that is inside the Samson Studio GT4, then that is perfect. You will need to setup your DAW (FL Studio) with whatever audio driver is recommended by Samson. There is nothing extraordinary that you need to do with the Motif ES in order to route audio to your DAW.
MIDI communication can be handled by either USB or an external MIDI interface to your computer. If you are seeing MIDI data routed into your DAW, but are not hearing it.. that is fairly typical as the problem is NOT the MIDI data. It is your audio routing scheme that has the problem.
Sorry we do not know FL Studio nor do we know the GT4, so you have to check on those yourself.
What you want to ensure is that the Motif ES is set to use MIDI IN/OUT = USB, and that you have the proper driver and version for your computer. You say you have the Motif driver, there is technically speaking no such thing.. the name of the driver is the Yamaha USB-MIDI driver V3.1.4 for Windows. If you see MIDI arriving, most likely you have the correct driver and you have it working properly.
The reason you are not hearing sound is a function of the Motif ES responding to returning audio and that audio going to your audio interface. Make sure that you have a MIDI track in your DAW set to 'echo back' (some times called 'thru' the data back to the Motif ES. And that the Motif ES can play through your speakers when that track is selected.