Remote mode means to connect to an existing Flink cluster (e.g. Flink standalone cluster). Besides setting FLINK_HOME and flink.execution.mode, you also need to configure flink.execution.remote.host and flink.execution.remote.port as the JobManager rest api address(Zeppelin submit flink job via JobManager's rest api). Here's a sample configuration screenshot.
After the configuration, you can also run the wordcount example to verify it.