Bulk Insert Permissions Issues
BULK INSERT always impersonates Windows logins for file access.  But your configuration is a double-hop, so Kerberos would be required for impersonation.  So, as stated, you are stuck.

Common workaround is to create a Credential and a SQL Agent Proxy, and kick off the load from a cmdexec or powershell SQL Agent job step.  Agent will use the stored credentials to logon locally and run the job, so it's no longer a double-hop.

A TSQL job step won't work as the credentials aren't used to LogonUser in that case, Agent just connects as the Agent Service Account and does SQL Server impersonation of the job owner.  

You can also access the file from the application server and either copy the file to the database server, or drive the bulk load from the client, eg with BCP or SqlBulkCopy.