Android - How can I make a button flash/blink?

There are several, depending on what kind of flashing you mean. You can, for example, use alpha animation and start it as your button first appears. And when the user clicks button, in your OnClickListener just do clearAnimation().

Example:

public void onCreate(Bundle savedInstanceState) {
    final Animation animation = new AlphaAnimation(1, 0); // Change alpha from fully visible to invisible
    animation.setDuration(500); // duration - half a second
    animation.setInterpolator(new LinearInterpolator()); // do not alter animation rate
    animation.setRepeatCount(Animation.INFINITE); // Repeat animation infinitely
    animation.setRepeatMode(Animation.REVERSE); // Reverse animation at the end so the button will fade back in
    final Button btn = (Button) findViewById(R.id.your_btn);
    btn.startAnimation(animation);
    btn.setOnClickListener(new OnClickListener() {
        @Override
        public void onClick(final View view) {
            view.clearAnimation();
        }
    });
}