Is this a common expression in German? In a practical sense, if you were to actually say this, would you mean "In general I do not have desires; I am an emotionally vacant robot" or is it it like, if someone asks you what you want to do this weekend, and you shrug "Ich habe keine Wünsche", to mean "I don't really mind"?
I don't think this is common in German. The closest you would get is the obligatory 'Haben Sie sonst noch einen Wunsch?' at your local bakery. But that rather means 'Do you want anything else/additional?'. One might also be 'wunschlos glücklich', perfectly happy. I guess, this sentence is just a bad, random example after all. If you took it literally and asked for my personal opinion, I would say it could either mean, you have no more desires or wishes above your quite good life or you really stopped wishing or hoping or dreaming, since you have always been disappointed whenever you did.
I just got the following, which is an error in the software (or the data the software is looking at):
The audio was correct and played "Ich habe keine Wuensche" (Sorry can't remember how to get umlaut's from a uk keyboard).
When I clicked on the button to record myself, it accepted me saying "Ich habe keine Wuensche"
However: The text displayed (not the hints, but the actual German text displayed on screen which you are meant to say and pronounce) says "I have none Wishes." That's not some dodgy translation from me, the actual text displayed for me to speak was "I have none Wishes".