TGifImage has such an array built in, so just make use of it:
var
Gif:TGifImage;
PaletteIndex : byte;
begin
Gif := TGifImage.Create;
// ... load your stuff here ...
// TGifImage has an Images property, which is probably only interesting if you're dealing with animations, so just take the first image.
PaletteIndex := Gif.Images[0].Pixels[0,0]; // palette index for top-left pixel
// Now, to get the actual TColor for that pixel, you could do this:
Self.color := Gif.Images[0].ColorMap.Colors[PaletteIndex];
end;