ここに書いてあるとおり以下のように書くとうまく動かない

"recipe[database::mysql]",
"recipe[mysql::server]",
"recipe[zabbix]",
"recipe[zabbix::database]",
"recipe[zabbix::server]"

こんなエラーがでる。

Chef::Exceptions::RecipeNotFound
--------------------------------
could not find recipe database for cookbook zabbix

これはドキュメントが古くて、zabbix::databaseをzabbix::mysql_setupとすればうごくようになる

また、db関連の設定もdatabase以下ではなくserver以下にかく

{
    "recipes":[
        "database::mysql",
        "mysql::server",
        "mysql::client",
        "zabbix",
        "zabbix::mysql_setup",
        "zabbix::server",
        "zabbix::web"

    ],
    "zabbix": {
        "agent": {
            "branch": "ZABBIX%20Latest%20Stable",
            "version": "2.2.1",
            "source_url": null,
            "install": true,
            "install_method": "prebuild",

            "servers":  ["localhost"]
        },
        "server": {
            "branch": "ZABBIX%20Latest%20Stable",
            "version": "2.2.1",
            "source_url": null,
            "install": true,
            "install_method": "source",
            "db_install_method": "mysql",
            "dbname": "zabbix",
            "dbuser": "zabbix",
            "dbhost": "localhost",
            "dbpassword": "zabbixpass",
            "dbport": "3306"
        },
        "web": {
            "install": true,
            "fqdn":  "localhost"
        }
    },
    "mysql": {
        "server_root_password": "iloverandompasswordsbutthiswilldo",
        "server_repl_password": "iloverandompasswordsbutthiswilldo",
        "server_debian_password": "iloverandompasswordsbutthiswilldo"
    }
}