Which are the minimum privileges required to get a backup of a MySQL database schema?
According to the MySQL Documentation


  mysqldump requires at least the SELECT privilege for dumped tables, SHOW VIEW for dumped views, TRIGGER for dumped triggers, and LOCK TABLES if the --single-transaction option is not used. Certain options might require other privileges as noted in the option descriptions.


Thus, to run 

mysqldump --no-data --routines --triggers ...


the privileges required are


SELECT 
SHOW VIEW (If any database has Views)
TRIGGER (If any table has one or more triggers)
LOCK TABLES (If you use an explicit --lock-tables)


You will also need the SELECT privilege on mysql.proc in order to dump Stored Procedures.