To reproduce: 

            this.radBrowseEditor1.Value = @"D:\Projects";
            this.radBrowseEditor1.ReadOnly = false; 
            this.radBrowseEditor1.BrowseElement.ShowClearButton = true;

You will notice that the clear button is not shown.

Workaround:

            LightVisualButtonElement btn = new LightVisualButtonElement();
            btn.Text = "X";
            btn.Click += btn_Click;
            btn.StretchHorizontally = false;
             
            this.radBrowseEditor1.BrowseElement.BrowseButton.Parent.Children.Add(btn);


        private void btn_Click(object sender, EventArgs e)
        {
            this.radBrowseEditor1.Value = null;
        }