There is no exact way you can access files just like web apps via Kudu Console. In order to access Cloud service files, you can enable a Remote Desktop connection in your role during development by including the Remote Desktop modules in your service definition or you can choose to enable Remote Desktop through the Remote Desktop Extension.
For more details, refer to Enable Remote Desktop Connection for a Role in Azure Cloud Services.
I would like to see the deployed files in azure portal now
As far as I know it is not supported by azure portal now. Azure cloud services allow us to remote the could services role, so we could remote the service to get the deployed files. About how to remote the cloud services role please refer to the azure document. We could see the published website under the IIS and we could get the physical path of files on the azure. More details please refer to the screenshot.
The Architecture Design of Cloud service is different then App Service. Cloud Service is hosted on its own dedicated environment. Cloud Service is NOT hosted on Shared Server like App Service.
When you create package for the Cloud Service. it contains all information of it's roles, Size of roles, number of instances per role and what files needs to be hosted on that role. ( Other information also).
if you have multiple roles in your cloud service. there will be dedicated VM for each instance of the Role. so your files will be placed on each role of that VM.
if you want to change any file from the deployment, you need to change it on all instances. Remember that if you restart the Cloud Service or Role all changes made in the file will be lost. Cloud Service will restore the old files. ( files at the time of deployment).
you can enable the remote login for roles and check the files.
if you want to know more about cloud Service check : http://avipatils.blogspot.in/
