I actually found it was easy, or at least automatic. For me at least - let me tell you my spec and what i just tested
Iphone7
Connected to Wifi / 4G - turned on the Fly app and brought map up full screen - zoomed in to decent street level accuracy. Then scrolled aroud the area methodically. Did same with just map view and also with satellite view
Completely closed the app
Turned wifi off and put phone to Airplane mode.
Restarted Fly app and brough map up. The street level detail is all there an even when I scroll around - in fact a larger area than I scrolled, but eventually the mapping runs out (quite a margin around though in some directions).
Satellite was just confined to a small local area.
From what I can summise (and I might be wrong), the iPhone at least is caching Google Maps tiles and remembering them. It's also cashing smaller areas of satellite. Also not sure how long it retains them
So it seems to me that just by connecting to Internet, browsing maps of where you want to fly, that the app remembers them.
(EDIT - just tried that process again but with satellite view - only this time zoomed in very close. Panned about. The images are there with the phone in Airline mode...)