Run all of the raw sources into FL Studio, not OBS, and then run the final soundtrack from FL Studio to OBS as OBS's only audio source at all. You probably knew that much already. The sticking point is getting it from FL Studio to OBS, right?
To do that, you'll need a loopback of some kind. So FL Studio thinks it's driving a speaker, and OBS thinks it's listening to a mic, but they're actually connected to each other. Here's one that's popular on this forum:
VB-Audio Virtual Cable and App's
vb-audio.com
Install that, send FL Studio to the virtual speaker that it creates, and have OBS pick up the virtual mic. Now you should have FL Studio feeding OBS.
You might also want to install another loopback (scroll down the same page) for OBS to feed FL Studio. That's for videos and other soundtracks that you can't easily get out of OBS. Use OBS's Monitor to send those through the second loopback to FL Studio, and not to the stream or recording. Mix everything in FL Studio, and send the final result back to OBS to stream and/or record. Don't Monitor that return in OBS! Only stream/record it.
Also, feed your headphones or studio monitors from FL Studio, not from OBS.
