Moving holograms it's really simple. Just use the teleport(Location loc) method.
Example
A hologram that follows a player above his head for 5 seconds.
// Suppose that we have already a Player object called "player"
HolographicDisplaysAPI api = HolographicDisplaysAPI.get(plugin);
final Hologram hologram = api.createHologram(player.getLocation().add(0.0, 2.0, 0.0));
hologram.getLines().appendText("Chat > Hello World");
new BukkitRunnable() {
// We don't want the task to run indefinitely
int ticksRun;
@Override
public void run() {
ticksRun++;
hologram.setPosition(player.getLocation().add(0.0, 2.0, 0.0));
// 100 ticks = 5 seconds
if (ticksRun > 100) {
hologram.delete();
cancel();
}
}
}.runTaskTimer(plugin, 1L, 1L);