What sort of SPN / AD Computer Delegation do you need for delegation of credentials to a linked server that connects to a file share?
There is only a single kind of Service Principal Name you need for SQL Server.  

MSSQLSvc/&lt;servername&gt;:&lt;portname&gt;


It is typically necessary to implement this twice, one for the short name, and one for the long name.   If, for instance, the SQL Server is named "SQLServer1.somedomain.com" and was running on port 1433, then you'd need:

MSSQLSvc/SQLServer1.somedomain.com:1433
MSSQLSvc/SQLServer1:1433


The computer account for SQLServer1.somedomain.com in Active Directory should be granted the ability to delegate security.  Once that is working correctly, you can confirm Kerberos authentication is working by looking at:

SELECT InstanceName = @@SERVERNAME
    , InstancePortNumber = dec.local_tcp_port
    , dec.auth_scheme
FROM sys.dm_exec_connections dec
WHERE dec.session_id = @@SPID;


If this shows Kerberos in the auth_scheme column, then Kerberos authentication is working.  If you have a second SQL Server at the other end of a linked server, you can run that query over the linked server:

DECLARE @cmd NVARCHAR(MAX);
SET @cmd = 'SELECT InstanceName = @@SERVERNAME
    , InstancePortNumber = dec.local_tcp_port
    , dec.auth_scheme
FROM sys.dm_exec_connections dec
WHERE dec.session_id = @@SPID;
';
EXEC [linked_server_name].tempdb.sys.sp_executesql @cmd;


The error message makes me think you're seeing a problem with file share permissions - when using Kerberos SQL Server will impersonate you when accessing the SMB share -  therefor your account needs access to it.