How to set FTP to a Azure Cloud Service or Azure storage?
The simplest solution I see would be to create an IaaS VM in azure and install an FTP server on it. Create the appropriate external endpoint and open up the firewall on the machine just like you'd do for an FTP server in your office.
For storage in the VM, you can attach a data disk that will live in your storage account. Make that data disk the file store for your FTP server and you should be good to go.