type
  TForm1 = class(TForm)
    Timer1: TTimer;
    ImageList1: TImageList;
    VirtualStringTree1: TVirtualStringTree;
    procedure Timer1Timer(Sender: TObject);
    procedure VirtualStringTree1GetImageIndex(Sender: TBaseVirtualTree; Node: PVirtualNode;
      Kind: TVTImageKind; Column: TColumnIndex; var Ghosted: Boolean; var ImageIndex: Integer);
  private
    FFrameIndex: Integer;
  public
    { Public declarations }
  end;

implementation

procedure TForm1.Timer1Timer(Sender: TObject);
begin
  // your GIF image has 12, which is that magic 12 here
  FFrameIndex := (FFrameIndex + 1) mod 12;
  // you can invalidate only certain nodes with InvalidateNode method
  VirtualStringTree1.Invalidate;
end;

procedure TForm1.VirtualStringTree1GetImageIndex(Sender: TBaseVirtualTree; Node: PVirtualNode;
  Kind: TVTImageKind; Column: TColumnIndex; var Ghosted: Boolean; var ImageIndex: Integer);
begin
  // if the tree requests image kind different from overlay, give it the current frame index
  if Kind <> ikOverlay then
    ImageIndex := FFrameIndex;
end;