What are the contributions of the Alchemists to the science of chemistry?
I think we would have to say it was limited, or none, because alchemy is not a scientific, but a mystical discipline.
Alchemy was a popular, but occult (hidden) study in the West so anyone practicing it would be likely to keep their apparent opposition to Christian teaching very private. They were also jealously guarding any “knowledge” they had as the first to discover how to change base metal into gold was certain to become the richest, hence most powerful, person on Earth.
Science, including Chrmistry, advances because people (like on this website) share their findings, allowing all to progress further. It is also rooted in a positivist, sometimes reductionist, paradigm relying on analytical thought to produce hypotheses that are then tested against reality in experiments. (Rutherford’s famous quote ‘demonstrate or die!’ is pertinent here.)
Because they relying on different methods to reach understanding, the field of alchemy contributed very little. It is interesting to note that the conversion of one element into another, first achieved by Rutherford and Soddy earned them the 1908 Nobel Prize in Chemistry, but concerned the conversion of nitrogen into oxygen, not lead into gold.