There are two components include in Delphi XE6 Firemonkey for accessing cloud services by Amazon and Microsoft. Additionally, there are two demos (here and here) that ships with Delphi XE6 Firemonkey that shows how to use these components to transfer files between your application and Amazon S3 or Azure Blob Service. The demo itself uses VCL but the cloud services are implemented in units that should compile in both VCL and FMX applications. For Azure the following components are available: TAzureBlobService, TAzureQueueService, TAzureTableService, and TAzureConnectionInfo. For Amazon S3 the following components are available: TAmazonTableService, TAmazonQueueService, TAmazonStorageService, and TAmazonConnectionInfo. Both the Azure and the Amazon APIs use REST and return XML which you can either parse yourself or use the built in functions. I believe you can use these components from all Firemonkey platforms (Windows, OSX, Android, and IOS) but OpenSSL is required. If you want access to more cloud providers there is also a cloud component pack for Firemonkey from TMS Software.
Check out the Developing Cloud Applications section from Embarcadero for more information on these components.
So this is writing a client solution… Can you also write an application in Delphi and deploy that to the “cloud”?