Imagine that your life is a journey. You begin your journey with your birth and you finish your journey with your death.
Your destiny is the path that your journey takes. Especially the part that you have not yet travelled. Like a path, your destiny is something that you follow.
Fate is the way that something ends up. For people, more specifically, our fate is the way we die. When we die, we reach our fate.
Fortune can have various meanings. It can mean 'luck', it can mean 'wealth', and it can mean something similar to 'destiny'. Fortune-tellers and fortune cookies can tell you about your future path, that is, your destiny.