You can try handling SelectedIndexChanged event and clearing the
selection there. This got rid of the selection after the click for me,
but there still was a temporary selection that flashed as you click
the checkbox. This code just removes it immediately.

private void checkedListBox1_SelectedIndexChanged(object sender,
EventArgs e)
{
    int index = checkedListBox1.SelectedIndex;
    if(index > -1)
    {
        checkedListBox1.SetSelected(index, false);
        checkedListBox1.SetItemChecked(index, !
checkedListBox1.CheckedIndices.Contains(index));
    }
}

================
Clay Burch
Syncfusion, Inc.