What do gluons have to do with chemistry?

Nothing.

Chemistry is the study of how atoms combine with other atoms. Gluons are force carrying particles that hold quarks together to form protons and neutrons in atomic nuclei.

While we would not have atoms without gluons, gluons do not participate in the reactions that join atoms together to form molecules. What holds atoms together is the electromagnetic force, in the form of positive charges in the nucleus, and negatively charged electrons.

Electrons move easily from one atom to another. Protons (hydrogen nuclei) are easily exchanged in reactions between acids and bases. But gluons stay inside the nucleus, and don’t play any part in sticking one atom to another.