Only part of the Burj Khalifa is open to the public and you can climb to part of the top of the Burj Khalifa where there are publicly accessible observation decks that the public can access.
The Burj Khalifa has another observation deck way at the top of the Burj Khalifa but it's not accessible or open to the public for safety reasons.
The very tip top floor of the Burj Khalifa is the 163rd floor which is the floor that the public cannot access but other floors the public can access.
So no you cannot go to the tip top of the Burj Khalifa which is a shame as it would be nice to climb to the tip top of the very lovely building which is the Burj Khalifa.