Azure file storage (AFS) supports both SMB 2.1 and 3.0 for file share access. The port 445 should be opened between source and AFS storage. There is a limitation when it uses SMB 2.1. Windows server 2008 and windows 7 machines uses SMB 2.1 protocol. So if source server is windows 7 or windows server 2008 then you can map AFS to the servers which are in same region to AFS storage account.
If you still want to copy the files to AFS then you can use azcopy.
c:\azcopy\AzCopy>azcopy.exe /source:c:\test /dest:http://storageaccountname.file.core.windows.net/logbackup /destkey:Storage primary/secondary key