I was struggling with the same problem and surprised that there wasn't a readily available answer...but finally got this figured out--at least for me anyway, and suspect it may be your problem as well. When setting up the application, I declined most of the accesses requested, and later found that things don't quite work as they should. For example, the AR capability obviously needs access to the camera. Well, turns out that to store pictures, it also needs access to "Storage". Go to Settings/Applications/Application Manager/Pokemon Go/Permissions. Turn on Storage...mine was off and that was what kept pics from being stored. With that turned on (along with Camera & Location), then it works great--in AR mode, press the camera icon and then the round button to capture the scene. Pics show up in the Gallery under a PokemonGo folder.
Hope that helps! :^)