If the .apk size is 900kb in the store, it's possible that Flappy Bird use Android "APK Expansion File" so that additional content is downloaded at runtime the first time you launch it.

Next, if you have very few graphics that always repeat (if I remember well Flappy Bird has very few graphics asset) they come compressed in the .apk and expended in memory during execution. Graphics asset are the files that more impact on final .apk size together with sound files.

Unity load a lot of stuff he need, but if you program the game directly in OpenGL you are able to cut your code and libraries to the essential and achieve very small packages.
I remember the time when Adventure Games (like maniac mansion) were all in one floppy disk.