How to take a flash/no flash picture with nikon d5600?

I used to own a Nikon way back in the day that allowed a picture that captured an image first with flash and then without flash, to both light up the subject while getting the ambiance in the background at the same time. Is there a setting on the new D5600 that I can do the same thing?

Get adobe after effects you noob.

What you're talking about is fill flash. In auto or P modes, the camera will fire the flash when needed. When it does, the camera will not try to balance the light coming from the flash with the ambient light.
This all changes when shooting in either shutter or aperture priority. In Av or Tv modes, when the camera fires the flash it will try to use an exposure that balances the light from the flash with the ambient light.

Aperture controls the exposure for the light coming from the flash. Shutter speed controls the exposure for the ambient light. So what your camera will do is use an exposure along with controlling the flash's output so that the ambient light and the flash light are balanced. But again, this will only happen when using shutter or aperture priority.

But I do think he is wrong on one point. I'm MOSTLY sure, but not 100% positive, that when in P mode, the flash will NOT pop up automatically. I think it only does that in the full Auto mode. It is simple enough to test and try. When indoors with the camera in Auto, (and in dim enough conditions that the flash will open), take a photo in which the flash opens by itself. Then, CLOSE THE FLASH, put the camera in P mode, and try taking the same photo in the same location / light. I think you will see that the flash will NOT open. The camera will take the photo using only ambient light. Manually opening the flash will cause it to function in the fill flash mode, (as will using Shutter or Aperture Priority modes).

Look at the mode dial of your camera. Under the Auto setting is a lightning in a circle with a bar across it. That means "no flash".

You can always try the the Slow-Sync and Rear-Curtain Sync flash settings on your camera on your camera. The first one leaves the shutter open after the camera has flashed to capture the ambient light, Rear curtain sync will expose for the ambient light and just before the shutter closes fires the flash.

I hope that's what you were looking for (and your camera has that setting)

Have fun!