You can't do that on RDS.
FLUSH [LOCAL] TABLES WITH READ LOCK;
is not supported. My assumption is that it might interfere with whatever their "rdsadmin" user (visible in the processlist) is doing to monitor or manage your instance.
If you're trying to use mysqldump, then --single-transaction
is the way to go:
https://forums.aws.amazon.com/thread.jspa?threadID=57642#
Otherwise, if you're trying to block writes, the only option I know would be to lock all of the tables manually or with an automated script that can enumerate the tables and acquire the locks.