How to secure SQL Agent Job that INSERTS to a linked server
SQL Express doesn't have SQL Agent, so I'm assuming you're running the job on the EE Server.

In that case, you should be able to simply use a TSQL job step on the SQL EE box 
The SQL Server Agent Account on the EE server already has rights to the local SQL Server.  You can grant it access to the remote SQL Express server.  If running under Network Service or a local virtual account, you would grant the rights to the computer account of the EE server.  EG

CREATE LOGIN [MyDomain\SQLEEComputerName$] FROM WINDOWS


Pushing data over a linked server is not very fast, however.  Pulling is faster.  So you'll need to test the performance.