It could be that there are no slow queries on this server yet. I have only gotten into one situation where I really needed to log slow queries, so I could hunt down who needed to index. Perhaps post the information about the version of OS and version of MySQL you are running on both the one that works and the one that doesn't so we can look for differences.
Pardon the second post seconds after the first, but it is early in the morning and often I have to read something several times for it to completely sink in. So the file (empty or not) does not create. I would also want to know the ownership and permissions of the /var/log/mysql directory, perhaps in both the server that it works compared to the server that is not working, so we can see the differences. Perhaps check the mysql log file to see if there are any errors or messages related to this issue.
Also I believe you do not need to start the service with --log-slow-queries=/var/log/mysql/mysql-slow.log, due to the fact that you put it into the configuration file.