Hi mfannin,
I could not reproduce this on my iPhone 6, iOS 9.1, X-Plane mobile version 10.1.0(38). I know this sounds silly, but are you dragging the right direction? When flaps are at 0, if you touch the icon and drag up, nothing will happen, so make sure you touch the icon and drag your finger down towards the bottom of the screen. Sometimes it is also picky that you touch it exactly in the middle. I sometimes have issues with moving the view when I mean to grab the rudder icon, for example.