Fire capes can be received as "Very Rare" drops from King Black Dragons, the Kalphite Queen and Blue dragons. It is the only animated cape in the game and is untradable. If you drop it, it dissapears immediately. Fire capes are common along those who cannot/dislike skill capes or colored capes.
If you want to sell this/trade this to a friend simply just go to "Skillz" and make sure no-one is around and sell it in the shop. That is a very easy way to trade it.