public bool IsReadOnly {get;}

{
    //Add the style to the current project
    string stylePath = @"C:\MyStyles\MyStyle.stylx";
    //Note: Needs QueuedTask to run
    StyleHelper.AddStyle(Project.Current, stylePath);
    StyleProjectItem styleToCheck = Project.Current.GetItems<StyleProjectItem>().First(x => x.Path == stylePath);
    //returns true if style is read-only
    bool isReadOnly = styleToCheck.IsReadOnly;
}