For people with rooted android devices, you can find the local high score at /data/data/com.dotgears.flappybird/shared_prefs/Flappy.xml
The contents of that file look like this:
<?xml version='1.0' encoding='utf-8' standalone='yes' ?>
<map>
<int name="score" value="your score here" />
</map>
If you have root, you can modify this file to be whatever you want.
On a completely unrelated note, I have a score of 9001.