While interactions between Vitamin Di and Zinc are not well studied, Vitamin D Receptors (VDRs) are known to have zinc fingers in their DNA binding domains:
And studies seem to suggest that zinc is important for proper Vitamin D Receptor function: Studies also seem to suggest that zinc is very important in the immunei response against infectionsi:
Here's a news article on a recent study suggesting that zinc induces higher T cell activation, important for fighting viral and bacterial infections:
Zinc and immune function: the biological basis of altered resistance to infection
Here's the study summary article:
Other studies also seem to support these findings: