How do I allow non sysadmin accounts the ability to create/query linked servers in SQL Sever 2014?
According to Article: Access to the remote server is denied because no login-mapping exists. 

Need to specify User ID in the provider string if Non-SYSAdmin accounts are used. 

Example: 

EXEC master.dbo.sp_addlinkedserver 
    @server = N'MyLinkServerName',
    @provider = N'SQLNCLI',
    @srvproduct = 'SQLNCLI',
    @provstr = N'SERVER=MyServerName\MyInstanceName;User ID=myUser'