I'm new to WoW. I'm a Draenei priest. I have the ability to flash heal and need to heal crash survivors. I target them like I would for the general healing spell, but it doesn't work. It only heals myself. What am I doing wrong?

You're trying to heal them with a wrong spell, you shouldn't be using priest spells, but your Draenei racial spell called "Gift of the Naaru". Check your spellbook and you'll find it there (press "P").

Its an art!