Why the LoginFailures metric showing no data for RDS MySQL instance?

That appears to be an Aurora MySQL-specific metric. In general, for RDS the Cloudwatch metrics reflect the features of the management service and infrastructure but not the database engine. To observe the database engine-specific metrics you would use the tooling for that specific engine. See https://aws.amazon.com/premiumsupport/knowledge-center/failed-login-rds-mysql/ for an example.

For Aurora MySQL and Aurora PostgreSQL, since Amazon develops those engines in can modify them to emit metrics directly into its monitoring infrastructure.