Fortune has 2 meanings: One is weath or riches. But in comparing this word to Fate and Destiny, I would argue that Fortune is the other meaning in this case, which is luck, or being fortunate. For example, you were fortunate that you avoided the plague (clearly not wealth or riches).
I would say that Fate is something out of your control, it is just something that is going to happen no matter what. It can be seen as a way of dealing with things, with accepting how things turned out, by calling it fate.
But then Destiny, I would not call this the same thing as fate. I believe Destiny is something a person is capable of achieving, which must be worked towards (hence the phrase "Fulfill your destiny"). Destiny is what can become in the future, but only if it's worked towards. With your own efforts, and with some good luck (or good fortune), you work towards your destiny.