You cannot simply "download" private Arma 3 mods. You must earn access. Here is the standard path:
Private mods are community-created additions (addons) restricted to specific groups, servers, or individuals. Unlike public mods, you won't find them by simply searching the Workshop. Access usually requires being part of a particular Arma 3 Unit or knowing the developers personally. Why Modders Keep Their Work Private Arma 3 Private Mods
The existence of private mods is a point of contention within the Arma 3 community: You cannot simply "download" private Arma 3 mods