MySQL RDS Error 1062
If you cannot use the RDS CLI, set proper DB Parameters or other means to set slave-skip-errors=1062, you are better off just creating a read replica to make a new Slave from the Master then dropping the old Slave that had the 1062 error.

I have mentioned MySQL RDS Read Replicas in the past


May 21, 2013 : Best strategies to have a backup of an RDS MySQL database
Jul 25, 2012 : Scaling Percona datacenters: setup and replication


After creating read replica, you should make sure you are using INSERT IGNORE or INSERT ... ON DUPLICATE KEY commands on the Master to prevent duplicate keys from replicating to Slaves.