Direct trading between Game Boy (Color/Advance) games and Nintendo DS games is not possible due to hardware and communication differences:
The intended way to move Pokémon forward is via Pal Park (in Diamond/Pearl/Platinum/HeartGold/SoulSilver) which requires a Game Boy Advance cartridge inserted into a DS/DS Lite—not a DS game trading with a GB game. For modern play, use Pokémon HOME with supported titles.