How to hot-backup mysql slave database with read operations
Here is how I would do it (Similar to your suggestion)


Terminal 1: FLUSH TABLES WITH READ LOCK It is important to keep this session/terminal open till the end of the process. Wait till you get the message the tables are now locked.
Terminal 2: Create the snapshot. Depending on what technology you use, this may vary. LVM snapshot is a common one. 
Terminal 1: UNLOCK TABLES
Copy the files from the snapshot location


It is essential not to close terminal 1 before you are done with step #2.

Notice please that there is no need to stop the slave. 

This link would be very helpful. It explains with more details, using LVM.

HTH