FWIW, I'm not afraid of flying, but most motion-style video games make me ill even if I'm watching on TV, as I have balance problems. I am, however, deathly afraid of FALLING. I do enjoy Soarin', but there are tricks to reducing my issues, I find.
I like the ride, but I have to be a bit careful about how I sit. The primary trick is NOT to sit forward in order to look down at what is passing by under your feet; sit back and focus your vision slightly upward, so that those feet above you are just barely in your line of vision. The upholstery of the seats is strong mesh fabric, and over time they have developed a wee bit of sag in the seat. If you are a smallish person, this enables you to comfortably sit back into the seat and even fold your legs up criss-cross, which young kids very often do because it's more comfortable for them. I would advise that if you feel dizzy, don't close your eyes, but rather look right at your lap, because your lap won't move in relation to your eyes. The seat belts fit snugly, so feeling a sensation of falling OUT of the seat shouldn't happen if you are sitting back. (All of the seats in a single row move together, so you don't move away from or toward others in your party. The row does tilt slightly down in front at times, but if you are sitting well back in the seat that won't put you leaning forward, only level.)
Truth to tell, because it's a film, the only thing really under your feet is a motionless concrete floor, but that floor is pretty darned far away; the seat rows lift to 45, 30, and 15 feet off the ground, respectively. (For reference on another ride you may know, the long drop on Splash Mtn is 49 feet high.) I once made the mistake of sitting in the end seat of my row, and looked down to the side. Whew, that was a long way down!, but as soon as I sat back and put my eyes back on the screen, I was fine again. IMO, on Soarin, the best "view" is from the middle seat of the middle row, because that is the row pushed furthest forward into the horizontal curve of the screen, but you'll feel less grounded there than in the bottom row, which has that lovely view of feet!
How is your child in IMAX films? You might want to try going to see one locally to get a feel for the way the screen looks. (It's not quite the same because a regular IMAX doesn't curve in at the bottom much, but the top does.)
Also, my final trick isn't really of any use to me, but I find that it works really well for apprehensive children: search for hidden Mickeys. If a child's mind is busily engaged with hunting for them in a "scary" ride, they almost always forget to be afraid. (Hint: there are two hidden Mickey images in the new Soarin', both much easier to see than the one in the old film was.)