Do you want the short answer or the long one? Some viable options or the best one?
The long one.
I am worried here. There are toooooo many basic points on the question. So I am preparing a check list of points you must further investigate. I will just write a basic tip on each point.
No bokeh: What aperture gives bokeh and which not? Do not use a wide aperture. Small apertures more range of objects in focus.
What aperture is needed if the model is say 10 ft from your camera and the tunnel end is say 200 meters?: Aperture has nothing to do with this... Or probably yes if you are refering to the exact same thing as No bokeh.
If I use in-built flash, it takes a picture of model but then washes out the tunnel's: The flash does not do that. What is doing that is a bad exposure.
What is happening? If you turn on the built in flash, it reduces automaticly the shutter speed to 1/200. Period. If the exterior needs a shutter speed of 1/1000, now will be overexposed. So you need to adjust your ISO and aperture.
Some viable options
The most viable options is to use multiple exposures, for a Hdr technique.
I am totally against using the built in flash... It basicly sucks. You could put a modifier in front of it... but it stills sucks.
The correct one
As you have not a cheap camera... spend some more on an external flash (or two) and a remote trigger.
Aditionally buy a tripod for each flash and a difuser like an umbrella or a softbox. You can use an asistant and a sheet of paper. But an external fhash is a must.
The long one
Yo need to study the Exposure triangle, and how to balance diferent iluminants.