Tested with Zabbix 3.4.11 on CentOS 7.5.1804 with SELinux set to Enforcing.
Check https://github.com/zabbix/zabbix/tree/master/templates/db/mysql_agent for the latest information.

Zabbix provides a template for basic MySQL monitoring since Zabbix 2.2.0 with the Template App MySQL that is provided on a fresh install or on Zabbix.org - Zabbix Templates/Official Templates/2.2 when upgrading.

A few preparations need to be made on the MySQL host before the template will work after assigning it to the host:

• A MySQL login with at least USAGE grant needs to be added to the MySQL server.
• A .my.cnf file with the MySQL login with USAGE grant needs to be created for the zabbix user.
• Connecting to MySQL via Zabbix agent needs to be enabled in SELinux.

Zabbix 3.4(.11) already provides the required userparameter_mysql.conf needed as /etc/zabbix/zabbix_agentd.d/userparameter_mysql.conf which is included by default in /etc/zabbix/zabbix_agentd.conf.

Use the following steps to configure:

1. Log into the Zabbix server via SSH.
2. Log into MySQL:

   mysql -u root -p

3. Execute the following SQL statement to create the zabbix-agent@localhost user with a password:

   GRANT USAGE ON *.* TO 'zabbix-agent'@'localhost' IDENTIFIED BY 'PASSSWORD';
   FLUSH PRIVILEGES;

   Change the PASSWORD to the chosen (generated) password.

4. Exit MySQL:

   \q

5. The configured home directory for the zabbix user is /var/lib/zabbix/. This is also the directory where the default userparameter_mysql.conf expects to find the .my.cnf file. This directory does not exist by default, so create it now:

   sudo mkdir /var/lib/zabbix/

6. Create .my.cnf with a text editor (in this case vi):

   vi /var/lib/zabbix/.my.cnf

7. Fill .my.cnf with:

   [client]
   user = zabbix-agent
   password = PASSWORD

   Change the PASSWORD to the chosen (generated) password.

8. Correct the permissions on /var/lib/zabbix/:

   sudo chown -R zabbix:zabbix /var/lib/zabbix/
   sudo chmod 0750 /var/lib/zabbix/

9. Label /var/lib/zabbix/ as SELinux type user_home_t:

   sudo chcon -Rt user_home_t /var/lib/zabbix/

10. Now SELinux needs to be adjusted to allow connecting to MySQL from Zabbix agent.
11. Save the following as “zabbix_agent_mysql.te”:

    module zabbix_agent_mysql 1.0;
    
    require {
            type mysqld_etc_t;
            type mysqld_t;
            type user_home_t;
            type zabbix_agent_t;
            class unix_stream_socket connectto;
            class file { read open };
    }
    
    #============= zabbix_agent_t ==============
    allow zabbix_agent_t mysqld_etc_t:file { read open };
    
    #!!!! This avc can be allowed using the boolean 'daemons_enable_cluster_mode'
    allow zabbix_agent_t mysqld_t:unix_stream_socket connectto;
    allow zabbix_agent_t user_home_t:file { read open };

12. Compile the .te file to an SELinux binary policy module:

    checkmodule -M -m -o zabbix_agent_mysql.mod zabbix_agent_mysql.te
    
    # checkmodule:
    # -M,--mls
    #       Enable the MLS/MCS support when checking and compiling the policy module.
    # -m     Generate a non-base policy module.
    # -o,--output filename
    #       Write a binary policy module file to the specified filename.  Otherwise, 
    #       checkmodule will only check the syntax of the module source file  and  will  not  generate  a
    #       binary module at all.

13. Turn the binary policy module into a policy package:

    semodule_package  -m zabbix_agent_mysql.mod -o zabbix_agent_mysql.pp
    
    #semodule_package
    # -m --module <Module file>
    #       Policy module file to be included in the package.
    # -o --outfile <output file>
    #       Policy module package file generated by this tool.

14. Install the policy package:

    semodule -i zabbix_agent_mysql.pp
    
    # semodule:
    # -i,--install=MODULE_PKG
    #       install/replace a module package

15. Import the latest version of the Zabbix template Template App MySQL on the Zabbix server.
    1. On 2018-07-27 that is Template_App_MySQL-2.2.0.xml from Zabbix.org - Zabbix Templates/Official Templates/2.2.
16. Attach the Template App MySQL to the host to monitor.
17. Wait a few minutes and check if the 2 MySQL graphs on that host show data.

Sources:

• Stack Overflow - Template MySQL didn't get result in Zabbix
• ZABBIX Forums - mysql items not working
• A cleaned up .te file after 'sudo audit2allow -a -M zabbix_agent_mysql'.
• Zabbix Bugs and Issues - [ZBX-10782] EL7 zabbix-agent package mysql userparameter needs SELinux policy