Upgrade from Nikon D5200 to D4s?

My friend is going into professional animal photography and I told her that is too big of a jump because the D4s is so big and complicated.

You sound like you don't know your aperture from a hole in the ground. Being big and complicated are things people say who have no idea what they are talking about.
Have you considered the technical differences between the two and how they will work when used in specialized situations like taking fast-moving subjects? Have you considered that the D4s is a full-frame camera that will produce a look to the image that can't be duplicated by an APS-C camera? Have you considered how the D4s will remove the technical limitations found in the D5200 allowing your friend to get the shot as opposed to missing it with the D5200? Of course, these questions are rhetorical because if you had, you wouldn't be asking your question.
I had the same kind of reaction as yours from friends and family members when I decided to get back into photography and bought a Pentax 645D. Unlike your friend, I didn't upgrade, because I sold off all of my gear. Three years later and I still think it's the best camera for me and would buy it all over again even with the options available in today's market.

You know that the D4s is too big and complicated? How? If she gets good results from the D5200, she'll not be daunted by the D4s.

I'm certain that your friend has done her due diligence and has opted for the D4s for a reason or two. There any number of cameras she could have chosen but, instead, decided on the D4s for reasons that will make her job easier and yield better results in her capable hands. Don't you have confidence in her decision, her experiences and her knowledge? Have you, perhaps, considered that what MAY seem "so big and complicated" to you may well be comfortable in her capable hands?

If she can afford it why not? I assume she's comforable shooting in aperture/shutter priority or manual with the D5200? Because the D4 is far less complicated than the D5200 in terms of 'scene modes' etc. It only has PSAM.

Oh and she'll need an external flash if she shoots with flash - in common with all pro models, the D4 doesn't have an onboard flash, just a hotshoe.

All I would add is that she doesn't NEED to upgrade to full frame to produce 'professional' looking images. What she needs is good lenses, good lighting and a thorough knowledge of exposure and lighting. If she is upgrading because she is not happy with her current image quality and she thinks a D4 will magically give her better images then she is wrong. You get better images by learning not by spending.

If your friend is willing to study photography and dedicate time and effort in learning the craft then a D4 is excellent for the job.

If she is qualified to call her self a "professional photographer", then she should know what she needs and which camera will satisfy her needs.

Are you qualified to give an advise?

Yes, D4s is a large camera because vertical grip is a built-in part of the camera. Complicated? Not really? All those switches and buttons do exactly the same thing as some of the items in the menuing system on D5200. If someone is a pro, he or she needs to be able to quickly adjust and change the camera setting. No time to go through menu, down, down, ok, down ok. So many common functions are assigned to buttons.

Compared to D5200, D4s will acquire focus MUCH quicker. That may be important for animal photography. Also, low light capability of F4s is far superior to D5200. It is a fully professional level camera.

Can she handle it? She IS a professional, right?