Verify that an APK has been built from given source code
You can only do this with 
reproducible builds: 


  "A build is reproducible if given the same source code, build environment and build instructions, any party can recreate bit-by-bit identical copies of all specified artifacts."


So the app developer or the app store needs to be on board in order for it to work.
Otherwise your only option is to build it yourself.

One example of a developer who currently does this is Open Whisper Systems:
https://github.com/WhisperSystems/Signal-Android/wiki/Reproducible-Builds