You don't have to disable DXDraw. Just do as Traveler suggested. Move drawing code form OnKeyUp event to separate Draw procedure. (procedure you do all the drawing). When you draw in OnKeyUp event the selected menu is drawn only once which causes this blink.

Another suggestion. You don't have to call DXDraw.Flip each time you draw something. Call it only once after everything is already drawn. To make it more clear here is an example code

Code:
// This is not the best example of an efficient drawing procedure
// because one menu item is drawn twice - first time as normal
// and second as selected. I did it like this  to make it as simple
// as possible.
procedure TMain.Draw;
begin
 // Game Logo
 MenuImages.Items[0].Draw(DXDraw1.Surface,255,50,0); 

 // Draw Start New Game
 MenuImages.Items[1].Draw(DXDraw1.Surface,350,300,0);

  //Draw Options
 MenuImages.Items[2].Draw(DXDraw1.Surface,350,360,0);

  // Draw Exit
  MenuImages.Items[3].Draw(DXDraw1.Surface,350,410,0);
 
  //Draw selected menu
  Case Menuchoice of
    0 : MenuImages.Items[4].Draw(DXDraw1.Surface,350,300,0);
    1 : MenuImages.Items[5].Draw(DXDraw1.Surface,350,360,0);
    2 : MenuImages.Items[6].Draw(DXDraw1.Surface,350,410,0);
  end;
  //the flip is called when everything is drawn
  DXDraw1.Flip; 
end;
I hope it helps.