How to run a cold backup with Linux/tar without shutting down MySQL slave?
FLUSH TABLES WITH READ LOCK will not halt writes to InnoDB.

FLUSH TABLES WITH READ LOCK does NOT work with InnoDB (MySQL Forums)
How FLUSH TABLES WITH READ LOCK works with Innodb Tables (mysqlperformanceblog.com)
How fast is FLUSH TABLES WITH READ LOCK? (mysqlperformanceblog.com)

It may block access to writing to tables, but InnoDB will allow writes to ibdata1 to provide MVCC info for redo and undo logs.
Check out Map of InnoDB's Infrastructure

Please note the physical independence of a table from the ibdata1, and how log files are related.
Since the box is a Slave, you have two options :
OPTION #1 (Warm Backup)

Run STOP SLAVE;
Run FLUSH TABLES;
Run your Linux/tar
Run START SLAVE;

OPTION #2 (Cold Backup of Fully Committed Data)

Run SET GLOBAL innodb_fast_shutdown = 0;
Run service mysql stop
Run your Linux/tar
Run service mysql start

OPTION #3 (Cold Backup)

Run service mysql stop
Run your Linux/tar
Run service mysql start

EPILOGUE
Options #2 and #3 would be the better choices by far. What is the difference between them ?

OPTION #2 flushes all transactional changes out of ibdata1 and the transaction logs (ib_logfile0, ib_logfile1). This makes for a longer shutdown. However, you will have a faster mysql startup because InnoDB Crash Recovery would not need to be performed.
OPTION #3 lets you shutdown faster, leaving InnoDB in suspended animation (all transactional changes in ibdata1 and the transaction logs (ib_logfile0, ib_logfile1)). The transactional changes are applied on mysql startup during the InnoDB Crash Recovery phase.