I'll change this answer if my assumption turns out to be wrong but I think that you want a list of all the child objects that meet certain criteria, regardless of which parent they belong to. In that case, you can use SelectMany on the parent. That will get a list of values for each parent and concatenate them all into one list. You can then filter that flattened list:

permissionList.AddRange(driveFileList.SelectMany(f => f.Permissions)
                                     .Where(p => p.Domain == "domainhere.com"));

SelectMany will return a list of all children from all parents, then the Where filters that child list.
EDIT:
Actually, I just realised that you can have the Where outside or inside the SelectMany . I'm not sure that it would make any practical difference, as you have to check every child either way, but this would work too:

permissionList.AddRange(driveFileList.SelectMany(f => f.Permissions.Where(p => p.Domain == "domainhere.com")));

That will filter each child list and then concatenate, while the previous code would concatenate the full lists and then filter. This is closer to what you had originally, but the result would be the same and I think the performance should be basically the same too, not that you could notice any different unless the lists were huge.