I tried some of the answers here using the flags or System.exit(0), but for me it either didn't work or it resulted in weird behavior. Sometimes it would kill the app, but then immediately restart it. I realized that I should just be doing things more of the standard way using request and result codes.
Basically, in your parent activity, start your child activity with:
startActivityForResult(new Intent(this, ChildActivity.class), CHILD_ACTIVITY_REQUEST_CODE);
where CHILD_ACTIVITY_REQUEST_CODE is just a constant (static final) integer. Then in your child activity, when they press the exit button, finish the activity with:
setResultAndFinish(RESULT_CODE_EXIT);
where RESULT_CODE_EXIT is another constant (static final) integer. Then back in your parent activity, handle the result code and finish the parent activity too:
protected void onActivityResult(int requestCode, int resultCode, Intent data) {
if(requestCode == CHILD_ACTIVITY_REQUEST_CODE) {
if(resultCode != ChildActivity.RESULT_CODE_EXIT) {
finish();
return;
}
}
}