In certain exposure modes, the built-in flash on your Nikon D7200 is set by default to fire automatically if the camera thinks that the ambient light is insufficient. In other modes, you have to manually enable flash. Here's the breakdown:
Autoexposure mode, all Scene modes that permit flash except Food mode, and Color Sketch Effect mode: After you press the shutter button, the camera automatically pops up the built-in flash if it finds the ambient light insufficient. If you don't want to use flash, you may be able to disable it by changing the Flash mode to Flash Off, as explained in the next section.
P, S, A, and M modes and the Food Scene mode: You control whether the flash fires. To pop up the built-in flash, press the Flash button on the side of the camera. Don't want flash? Just press down gently on the top of the flash to close the unit. Except for when you shoot in the Food Scene mode, you also have the option of leaving the flash up and setting the Flash mode to Flash Off.
In P, S, A, and M modes (and the Food Scene mode), raise the built-in flash by pressing the Flash button.The camera keeps the flash charged as long as the unit is up, so to save battery power, close the flash unit when possible.
If the flash doesn't pop up as expected, the problem may be related to the aforementioned Flash Off mode. When this option is enabled, the flash won't come out of hiding no matter how many times you press the Flash button. Try pressing the Flash button while rotating the Main command dial, which changes the flash mode. If that fix doesn't work, don't try to pry the flash up; you could break it for good. Instead, head for a camera-repair shop.