Yeah that's pretty good. More natural to me would be: "I've got more chance of finding a unicorn than an English exchange partner" 'Of finding' doesn't need to be used the second time. Another way of saying the same thing would be "English exchange partners are like hen's teeth." Hens obviously don't have teeth so are very rare (nonexistent), so this statement basically means English language partners are very rare.

seems perfect to me.

That's written just as I would write it. Good job.