There is no LabVIEW function to do that. You will need to use an operating system function to do it. The method varies, depending on the operating system. On Windows you can use Windows API calls or you can just use the command line commands, such as attrib via System Exec.
As per my reasearch on the subject and as mentioned by Jeff and Smercurio, you need to make windows API calls to set the file access permissions programmatically.
A natural start would be use the "Call Llibrary Function Node" to make dll calls. The dll file that I believe would be relevant here is "advapi32.dll" located in system32 folder.
This dll would contain functions like "BuildExplicitAccessWithName()" which give explicit access for reading or writing for any windows object.
Though I could not find any relevant labview example code, the following links would be helpful to you.
