UNC paths can be tricky sometimes. Since you are using that, has it been set-up as a fileshare? The proxy account will need read write access to the share. If you have admin rights on the server that you are writing to (the fileshare) then you can set the share up yourself.

After you've verified that you can read and write to the share, try something simple like creating a package with a File System Task and see if you can move a file to the share in a SQL Agent job using the proxy to execute the job. If you can then you are in business.