Here is one of the smallest flip phones money can buy. The LONG-CZ J9 0.66″ Flip Phone has a 300 mAh battery that lasts for 4 days on standby. It connects to your smartphone to sync your calls, phonebook, and other activities. It can also remind you when you are about to leave your phone behind accidentally.
The J9 has a voice changer option, so you can talk in funny voices with others. It has a FM radio too. Pretty cheap too!