Running forms in Oracle Cloud Service
Forms is a Middleware product in and of itself - not a user-developed J2EE application. http://www.oracle.com/technetwork/developer-tools/forms/overview/index.html is the best start page here. This means that to deploy to the cloud, you will need to deploy to a supported stack with the application server and forms runtime in place. That, in turn, most likely means that you would need to be running a custom VM at your cloud provider. 

You mention as a reason access from anywhere. This is not a unique ability of the cloud. https://docs.oracle.com/middleware/12213/formsandreports/deploy-forms/using-oracle-forms-services-http-listener-and-oracle-weblogic-server.htm#FSDEP228 covers routing to forms via the HTTP Listener which you could locate in your own DMZ or in the cloud.