I found the solution. The problem was related to Sql Server Agent Job. Amazon RDS will not allow Sql Server Agent Job to be created as a part of Creation of AppFabric Montoring Database. But the Sql Server Agent Job can be manually created in Amazon RDS which will serve the purpose. The AppFabric Monitoring Database has 4 Sql Server Agent Jobs
The below jobs need to be manually Created in Amazon Rds Microsoft_ApplicationServer_Monitoring_AutoPurge_AppFabricMonitoringStore Microsoft_ApplicationServer_Monitoring_ImportTransferEvents_AppFabricMonitoringStore Microsoft_ApplicationServer_Monitoring_ImportWcfEvents_AppFabricMonitoringStore Microsoft_ApplicationServer_Monitoring_ImportWfEvents_AppFabricMonitoringStore