How to grant permission to view database audit logs to non-sysadmin login
Reference:


sys.fn_get_audit_file (Transact-SQL)
View a SQL Server Audit Log



  Microsoft recommends viewing the audit log by using the Log File
  Viewer. However, if you are creating an automated monitoring system,
  the information in the audit file can be read directly by using the
  sys.fn_get_audit_file (Transact-SQL) function. Reading the file
  directly returns data in a slightly different (unprocessed) format.
  See sys.fn_get_audit_file for more information.


In order to use sys.fn_get_audit_file users requires the CONTROL SERVER permission.

You can deny privilege on a principle who has been assigned CONTROL SERVER permission which is not possible in case of SYSADMIN.

More about this:

Security Questions: Difference between sysadmin and CONTROL SERVER Permission by Jason Strate.