To "flash" someone means to either deliberately or inadvertently show any part of your body that is ordinarily expected to be kept covered in that venue. It doesn't have to be genitalia, as we can talk about "flashing" an ankle or knee in countries where women don't ordinarily show those body parts.
In other words, "flashing" needs to be unexpected. You can't flash someone at a nude beach, for example, because it's a place where you expect to see naked people.
In this context, while entering the American Music Awards, Teigen flashed her mons pubis (the area above her genitalia) to a photographer standing to one side of her. Thus "side flash".