I'm not in this field, nor have I done any maths in a long time so my answer might be off by a long way but I felt like challenging myself so here it goes.

I'm going to use Hubble for my calculations because it's the popular kid that everyone knows about. There are probably much better choices of camera that can be made for doing this kind of task.

http://i.imgur.com/RtGPJP4.jpg

First thing to keep in mind, Hubble was not designed to take photographs of very close objects, so it has a pretty narrow field of view. Which means it would have to be pretty far back in order for it to be able to take a picture of the milky way in one exposure.

It's Wide Field Camera 3 has a field of view of 164 arcsec's. Or 0.0456 °. The Milky Way is an estimated 100,000 - 120,000 Light years across. I will use 100,000.

If you plug in those numbers and do some trigonometry you get 125,648,632.65 Light years as your answer for how far away you would have to be in order to take a top down picture of the milky way. Considering we can only travel at a tiny fraction of the speed of light it's very doubtful that we will ever get a top down picture of the milky way in our lifetimes.

There are, however, a few tricks you can do to shorten that distance substantially. The Hubble has taken beautiful pictures of the Andromeda galaxy. That galaxy is 220,000 Light years across, however it's only a mere 2,500,000 Light years away. So how is it that Hubble can take such a wide shot of Andromeda from such a relatively short distance? It takes a panorama of course! That wide, lovely image of Andromeda was taken by combining 7,398 exposures taken over 411 individual pointings.

http://imgsrc.hubblesite.org/hu/db/images/hs-2015-02-a-hires_jpg.jpg

So in short you wouldn't really have to be as far away as my calculation suggests in order to take a picture of the whole galaxy. You can be much closer and still get a wide, encompassing picture of our galaxy from much closer distances. The one thing you would have to keep in mind however is that the closer you are to any part of the galaxy the more distortion your image will have. The relative distances of the stars you're closer to are going to be larger in your FOV than those parts which are further away. It will make our galaxy look like its bulging or distorted, like a fish eye lens.

I think the best way we can currently take an image of our galaxy would not to send out a camera to take a snapshot, but to make a large map of all the locations of stars and gasses etc and then render those maps into an image. Unfortunately our own galaxy has a lot of matter and stuff in it which blocks us from seeing everything though, from this vantage point anyway...