how to run command "mysqladmin flush-hosts" on Amazon RDS database Server instance?

For normal MySQL, just connect as the 'root' administrative super user, and issue the command:

FLUSH HOSTS

Even in the case of too many connections, MySQL should be keeping a connection in reserve so that a super user can connect.

The mysqladmin client generally connects as root anyway and issues the above SQL.

Login to any other EC2 instance you have that has access to the RDS instance in question and has mysqladmin installed and run

mysqladmin -h <RDS ENDPOINT URL> -P 3306 -u <USER> -p flush-hosts

you will be prompted for your password

When an Amazon RDS instance is blocked because the value of max_connect_errors has been exceeded, you cannot use the host that generated the connection errors to issue the "flush hosts" command, as the MySQL Server running on the instance is at that point blocking connections from that host.

You therefore need to issue the "flush hosts" command from another EC2 instance or remote server that has access to that RDS instance.

mysqladmin -h [YOUR RDS END POINT URL] -P 3306 -u [DB USER] -p flush-hosts

If this involved launching a new instance, or creating/modifying security groups to permit external access, it may be quicker to simply login to the RDS user interface and reboot the RDS instance that is blocked.