To set an alarm to wake you up, set your alarm up in the usual way on your connected phone. When this sounds in the morning, it will sound through your headphones.
If you have set your headphones to turn off when you remove them, and you do take your headphones off in the night, then your alarm will sound through your phone as usual.
Kokoon will also be releasing a Smart Alarm, which is still in development. You can read about this future feature here.